This document discusses proportionality and similarity. It includes diagrams showing proportional or similar figures with corresponding parts or ratios being equal. It also demonstrates calculating scale factors when converting between units like centimeters and kilometers.
The document describes different types of graphs including undirected graphs, directed graphs, and graphs with weights. For undirected graphs, it provides two examples with vertices A, B, C, and D and lists the edges between them. For directed graphs, it shows two examples where the edges represent a direction from one vertex to another. It also includes two examples of graphs with weights, where the edges have numerical weights assigned to them.
This document provides instructions for an activity to find the highest common factor (HCF) of two numbers experimentally based on Euclid's division lemma. The activity involves cutting strips of cardboard of different lengths to represent numbers, covering them in different colored paper, and arranging them according to the divisions in Euclid's lemma to visually demonstrate the HCF. Figures are provided to show how the strips should be arranged. The HCF is found to be the length of the final remaining strip. Observations of actual measurements are to be recorded to determine the HCF of the original two numbers.
The document is an exam for grade 8 mathematics students with 6 questions testing various math skills. Question 1 has 4 parts testing the solving of equations. Question 2 tests solving an inequality. Question 3 asks students to calculate the area of a rectangle given length and width ratios. Question 4 involves similar triangles to calculate the height of a building. Question 5 asks students to calculate the area of a plot of land given its dimensions. Question 6 has 3 parts testing properties of right triangles, including similarity, Pythagorean theorem, and symmetry.
1. The document discusses a library stock management system with entities like books, copies, readers, and loans. It defines relationships between these entities like what books are stocked, which copies are issued to readers, and overdue return dates.
2. Set theory concepts like intersection, union, subset, and complement are explained through examples like disjoint sets, inclusion relationships between sets.
3. An example algebraic expression is broken down step-by-step to show that a subset relationship holds true.
This document contains the results of a fractional factorial design experiment with 5 factors (temperature, material type, pressure, density, and oxygen level) investigated for their effects on total yield. It provides the results, defines the design generators and resolution, estimates the main effect of one factor and related ANOVA table, and asks questions about multicollinearity, variance inflation factors, outliers, and influential points.
This document is an assignment from a General Physics 101 course. It contains 6 multi-part physics problems involving vector addition and subtraction, finding magnitudes and directions of vectors, and using trigonometric functions to solve problems graphically and analytically. The instructor is Dr. Said Moh'd Azar.
This document discusses the representation of binomial expressions through geometric diagrams and algebraic formulas. It shows:
1) The expansion of the square of a binomial using diagrams and the formulas (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2.
2) The multiplication of two binomials with a common term using a diagram and the formula (x + a)(x + b) = x2 + (a + b)x + ab.
This document discusses proportionality and similarity. It includes diagrams showing proportional or similar figures with corresponding parts or ratios being equal. It also demonstrates calculating scale factors when converting between units like centimeters and kilometers.
The document describes different types of graphs including undirected graphs, directed graphs, and graphs with weights. For undirected graphs, it provides two examples with vertices A, B, C, and D and lists the edges between them. For directed graphs, it shows two examples where the edges represent a direction from one vertex to another. It also includes two examples of graphs with weights, where the edges have numerical weights assigned to them.
This document provides instructions for an activity to find the highest common factor (HCF) of two numbers experimentally based on Euclid's division lemma. The activity involves cutting strips of cardboard of different lengths to represent numbers, covering them in different colored paper, and arranging them according to the divisions in Euclid's lemma to visually demonstrate the HCF. Figures are provided to show how the strips should be arranged. The HCF is found to be the length of the final remaining strip. Observations of actual measurements are to be recorded to determine the HCF of the original two numbers.
The document is an exam for grade 8 mathematics students with 6 questions testing various math skills. Question 1 has 4 parts testing the solving of equations. Question 2 tests solving an inequality. Question 3 asks students to calculate the area of a rectangle given length and width ratios. Question 4 involves similar triangles to calculate the height of a building. Question 5 asks students to calculate the area of a plot of land given its dimensions. Question 6 has 3 parts testing properties of right triangles, including similarity, Pythagorean theorem, and symmetry.
1. The document discusses a library stock management system with entities like books, copies, readers, and loans. It defines relationships between these entities like what books are stocked, which copies are issued to readers, and overdue return dates.
2. Set theory concepts like intersection, union, subset, and complement are explained through examples like disjoint sets, inclusion relationships between sets.
3. An example algebraic expression is broken down step-by-step to show that a subset relationship holds true.
This document contains the results of a fractional factorial design experiment with 5 factors (temperature, material type, pressure, density, and oxygen level) investigated for their effects on total yield. It provides the results, defines the design generators and resolution, estimates the main effect of one factor and related ANOVA table, and asks questions about multicollinearity, variance inflation factors, outliers, and influential points.
This document is an assignment from a General Physics 101 course. It contains 6 multi-part physics problems involving vector addition and subtraction, finding magnitudes and directions of vectors, and using trigonometric functions to solve problems graphically and analytically. The instructor is Dr. Said Moh'd Azar.
This document discusses the representation of binomial expressions through geometric diagrams and algebraic formulas. It shows:
1) The expansion of the square of a binomial using diagrams and the formulas (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2.
2) The multiplication of two binomials with a common term using a diagram and the formula (x + a)(x + b) = x2 + (a + b)x + ab.
The document contains a math worksheet with 5 problems for an 8th grade student. Problem 1 asks the student's name. Problems 2-4 provide polynomial expressions and ask the student to calculate the sum and difference of the expressions. Problem 5 provides 3 more polynomial expressions and asks the student to perform various calculations combining the expressions using addition and subtraction.
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The document contains an assignment, warm-up problems, lesson notes on polygons, and examples from Lesson 19. The assignment is to complete Set 20 of even problems and it is due the next day. The lesson notes define polygons, regular polygons, congruent figures, similar figures, and dilation. Examples include identifying shapes such as hexagons, octagons, and dodecagons.
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This document describes how to use cut-out shapes to verify several algebraic identities through visual representation and calculation of areas. It provides instructions and materials for verifying the identities (a+b)2, (a-b)2, and a2 - b2 = (a+b)(a-b) using squares, rectangles, and other shapes cut out of paper or cardstock. Tables are included to record the values being tested and calculate both sides of each identity to check for equality. The goal is to visually and physically demonstrate several fundamental algebraic relationships using a hands-on math kit.
This document summarizes how to prove that the angle subtended by an arc at the centre of a circle is twice that subtended at the circumference, even when a line cannot be drawn through the centre cutting both angles. It does this by extending one arc line to the centre, then using properties of isosceles triangles and angles on a straight line to derive an equation that solves to the desired property.
This document provides a summary of key concepts in algebra, geometry, trigonometry and their definitions. It includes formulas and properties for lines, polynomials, exponents, trig functions, triangles, circles, spheres, cones, cylinders, distance and the quadratic formula. Key topics covered are factoring, binomials, slope-intercept form, trig ratios, trig identities, trig reciprocals and the Pythagorean identities.
jstse 2015 question paper with solution,
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This document summarizes how to prove that the angle subtended by an arc at the centre of a circle is twice that subtended at the circumference, even when a line cannot be drawn through the centre cutting both angles. It does this by extending one arc line to the centre, then using properties of isosceles triangles and adjacent angles to show that the central angle is equal to twice the angle at the circumference.
The document provides notes from a math lesson, including assignments due, warm-up problems to work on, and lesson content about polygons, regular polygons, congruence, similarity, and dilation. Examples are also given to identify different polygons and determine which figures are similar or congruent.
This document discusses calculating the surface areas of different 3D geometric shapes. It provides formulas for calculating the total surface area, lateral surface area, and volume of a cuboid with given length, breadth, and height dimensions. It also provides formulas for calculating the curved surface area and total surface area of a cylinder and sphere with a given radius.
I. There exist three consecutive terms of the sequence that form a geometric progression.
II. 7a is a prime number.
III. If n is a multiple of 3, then an is even.
The correct options that contain true statements are I, II, and III.
The document describes reflections and translations, which are types of transformations in geometry. It defines reflections as transformations across a line where corresponding points are an equal distance from the line. Translations are defined as transformations where all points of a figure are moved the same distance in the same direction, making them an isometry. Examples of reflecting and translating points and figures are provided to illustrate these concepts.
1. The diagram shows angles MBC and ABC measuring 25 degrees each.
2. Angle MBC and ABC are equal since they are vertical angles.
3. Therefore, the measure of angle CBD is also 25 degrees by angle substitution.
This document contains a 14 question multiple choice exam along with its answer key. The exam covers topics such as arithmetic progressions, polynomial functions, probability, geometry of polygons and triangles, matrices, and trigonometry. The answer key indicates that the correct answers are choices C, C, A, A, B, C, B, C, D, C, A, D, B, and B, respectively, for each question.
Computer Graphic - Transformations in 3d2013901097
1. The document describes the steps to perform a rotation of an object in 3D space about an arbitrary point or axis.
2. It provides an example of rotating a unit cube 90 degrees about an axis defined by two points and calculating the new coordinates.
3. It also gives an example of rotating the point (1,2,1) 90 degrees and showing the resulting point (1,2,3) transformed to (4,6,7).
The document discusses algebraic expressions using geometric representations. It represents the lengths a and b on a number line and draws the squares of a and b as a2 and b2. It also draws the rectangle with dimensions a and b, representing the expression ab. Finally, it derives the expansion of (a + b)2 and (a - b)2 using geometric representations of a, b, their sums and differences.
This document defines and provides examples for the usage of various prepositions of place in English. It explains prepositions such as by, down, up, out of, into, in, on, toward, away from, over, under, next to, between, behind, in front of, above, below, near, far, onto, off, around, along, across, and through. For each preposition, it gives a short explanation, example sentence, and 2-3 further example sentences to illustrate how that preposition is used to indicate spatial relationships between objects.
This infographic provides a pictorial explanation of essential English grammar concepts including the uses of modal verbs like may, can, must, and should. It outlines how may is used to request permission or indicate politeness, might indicates lower possibility than may, can is used for requests, abilities, and possibilities, must denotes obligations or high probabilities, and should is used for suggestions or advice. The infographic references an English grammar usage book as its source.
This infographic provides a pictorial explanation of essential English grammar. It summarizes and visually depicts the key tenses in English, including the present simple, present continuous, present perfect, past simple, past continuous, future simple, future continuous, and others. Examples are provided to illustrate the meaning and usage of each grammatical tense. The infographic is intended as a reference for understanding essential English grammar concepts.
The document contains a math worksheet with 5 problems for an 8th grade student. Problem 1 asks the student's name. Problems 2-4 provide polynomial expressions and ask the student to calculate the sum and difference of the expressions. Problem 5 provides 3 more polynomial expressions and asks the student to perform various calculations combining the expressions using addition and subtraction.
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
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The document contains an assignment, warm-up problems, lesson notes on polygons, and examples from Lesson 19. The assignment is to complete Set 20 of even problems and it is due the next day. The lesson notes define polygons, regular polygons, congruent figures, similar figures, and dilation. Examples include identifying shapes such as hexagons, octagons, and dodecagons.
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
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This document describes how to use cut-out shapes to verify several algebraic identities through visual representation and calculation of areas. It provides instructions and materials for verifying the identities (a+b)2, (a-b)2, and a2 - b2 = (a+b)(a-b) using squares, rectangles, and other shapes cut out of paper or cardstock. Tables are included to record the values being tested and calculate both sides of each identity to check for equality. The goal is to visually and physically demonstrate several fundamental algebraic relationships using a hands-on math kit.
This document summarizes how to prove that the angle subtended by an arc at the centre of a circle is twice that subtended at the circumference, even when a line cannot be drawn through the centre cutting both angles. It does this by extending one arc line to the centre, then using properties of isosceles triangles and angles on a straight line to derive an equation that solves to the desired property.
This document provides a summary of key concepts in algebra, geometry, trigonometry and their definitions. It includes formulas and properties for lines, polynomials, exponents, trig functions, triangles, circles, spheres, cones, cylinders, distance and the quadratic formula. Key topics covered are factoring, binomials, slope-intercept form, trig ratios, trig identities, trig reciprocals and the Pythagorean identities.
jstse 2015 question paper with solution,
jstse books,
jstse book for class 9 pdf,
jstse 2016-17,
how to prepare for jstse,
jstse 2015 answer key,
jstse exam sample paper for class 9,
jstse official website,
jstse previous year papers,
jstse,
This document summarizes how to prove that the angle subtended by an arc at the centre of a circle is twice that subtended at the circumference, even when a line cannot be drawn through the centre cutting both angles. It does this by extending one arc line to the centre, then using properties of isosceles triangles and adjacent angles to show that the central angle is equal to twice the angle at the circumference.
The document provides notes from a math lesson, including assignments due, warm-up problems to work on, and lesson content about polygons, regular polygons, congruence, similarity, and dilation. Examples are also given to identify different polygons and determine which figures are similar or congruent.
This document discusses calculating the surface areas of different 3D geometric shapes. It provides formulas for calculating the total surface area, lateral surface area, and volume of a cuboid with given length, breadth, and height dimensions. It also provides formulas for calculating the curved surface area and total surface area of a cylinder and sphere with a given radius.
I. There exist three consecutive terms of the sequence that form a geometric progression.
II. 7a is a prime number.
III. If n is a multiple of 3, then an is even.
The correct options that contain true statements are I, II, and III.
The document describes reflections and translations, which are types of transformations in geometry. It defines reflections as transformations across a line where corresponding points are an equal distance from the line. Translations are defined as transformations where all points of a figure are moved the same distance in the same direction, making them an isometry. Examples of reflecting and translating points and figures are provided to illustrate these concepts.
1. The diagram shows angles MBC and ABC measuring 25 degrees each.
2. Angle MBC and ABC are equal since they are vertical angles.
3. Therefore, the measure of angle CBD is also 25 degrees by angle substitution.
This document contains a 14 question multiple choice exam along with its answer key. The exam covers topics such as arithmetic progressions, polynomial functions, probability, geometry of polygons and triangles, matrices, and trigonometry. The answer key indicates that the correct answers are choices C, C, A, A, B, C, B, C, D, C, A, D, B, and B, respectively, for each question.
Computer Graphic - Transformations in 3d2013901097
1. The document describes the steps to perform a rotation of an object in 3D space about an arbitrary point or axis.
2. It provides an example of rotating a unit cube 90 degrees about an axis defined by two points and calculating the new coordinates.
3. It also gives an example of rotating the point (1,2,1) 90 degrees and showing the resulting point (1,2,3) transformed to (4,6,7).
The document discusses algebraic expressions using geometric representations. It represents the lengths a and b on a number line and draws the squares of a and b as a2 and b2. It also draws the rectangle with dimensions a and b, representing the expression ab. Finally, it derives the expansion of (a + b)2 and (a - b)2 using geometric representations of a, b, their sums and differences.
This document defines and provides examples for the usage of various prepositions of place in English. It explains prepositions such as by, down, up, out of, into, in, on, toward, away from, over, under, next to, between, behind, in front of, above, below, near, far, onto, off, around, along, across, and through. For each preposition, it gives a short explanation, example sentence, and 2-3 further example sentences to illustrate how that preposition is used to indicate spatial relationships between objects.
This infographic provides a pictorial explanation of essential English grammar concepts including the uses of modal verbs like may, can, must, and should. It outlines how may is used to request permission or indicate politeness, might indicates lower possibility than may, can is used for requests, abilities, and possibilities, must denotes obligations or high probabilities, and should is used for suggestions or advice. The infographic references an English grammar usage book as its source.
This infographic provides a pictorial explanation of essential English grammar. It summarizes and visually depicts the key tenses in English, including the present simple, present continuous, present perfect, past simple, past continuous, future simple, future continuous, and others. Examples are provided to illustrate the meaning and usage of each grammatical tense. The infographic is intended as a reference for understanding essential English grammar concepts.
This document discusses factorizing the difference of two squares. It shows that a2 - b2 can be written as (a+b)(a-b) by representing the terms geometrically. The document was animated by Abdul wasay Yusuf to demonstrate this factorization using visual representations.
Article review textbooks and the construction of militarism in pakistan naseem aMuhammad Yusuf
This article examines how Pakistani textbooks normalize militarism in society. The author defines normalization as establishing something as normal or standard through discourse. In Pakistan, textbooks promote militarism by including poems about historical Muslim warriors, stories of wars between Pakistan and India that emphasize soldier sacrifices, and learning objectives about threats from India. Examples from textbooks describe Hindus as enemies and say the Hindu religion does not teach good things. The author argues this indoctrinates militarism as normal and can be seen in Pakistani society's lack of tolerance for dissent and support for jihadi groups.
The document provides examples and steps for multiplying, dividing, and solving word problems involving fractions using visual models. It includes worked examples of multiplying fractions like 4 × 2/3 and 1/4 × 2/3 as well as dividing fractions such as 2/5 ÷ 2/3 and 3/4 ÷ 2/3. Additional word problems involve sharing a pizza between people, making cakes from a bottle of oil, and determining fractions of flowers or people at a convention.
Decagonal approach, a vehicle for school improvementMuhammad Yusuf
The decagonal approach is a school improvement model used in Pakistan that takes a whole school approach rather than just focusing on teachers. It involves 10 components: capacity building of teachers, leadership and management, community participation, children's participation, developing the physical environment, curriculum enrichment, research and documentation, school governance, school-based interventions, and local resource generation. The approach was implemented in 30 schools over 2 years. Key lessons learned include that school improvement is a process, not an event, it requires team effort and changing individual attitudes, and creating a conducive learning environment contributes to student learning.
This study examined factors that influence job satisfaction among secondary school teachers in Sindh, Pakistan. A survey was administered to 305 teachers to assess the impact of work-life balance, administrative support, salary, and teacher input in decision making on job performance and satisfaction. The findings showed strong correlations between work-life balance and administrative support with job satisfaction, but not salary or teacher input. No significant differences were found between male and female teachers. The study recommends improving work-life balance support and involving teachers more in decision making to boost job satisfaction.
Implications of the Gap Analyses of Children’s Literature in Pakistan and Vie...Muhammad Yusuf
3rd International Conference of the Linguistics Association of Pakistan (ICLAP)
Humanities Department NED University & Higher Education Commission
Karachi, Sindh, Pakistan October 12-14, 2017
With Dr. Valerie Haugen, International and Comparative Education SpecialistMr. Saeed Nasim, Language and Mathematics Education SpecialistMr. Muhammad Yusuf, Language Education Specialist
Teacher training model for single school teacherMuhammad Yusuf
An assignment presentation for my coursework with Zain, Noor, Shoaib, Imtiaz. This presentation shows our proposed model for training of single school teacher.
Cuisenaire rods were invented by Emile Cuisenaire in the early 20th century and popularized by Caleb Gattegno in the 1950s. The rods are integer-length blocks used to teach mathematical concepts like addition, subtraction, multiplication and division visually. The document provides examples of how to use the colored rods to represent and solve math problems involving these operations. It also covers fractions, area, perimeter and symmetry.
Scaffolding refers to support provided by teachers to help students learn and master new concepts and skills. Effective scaffolding strategies include motivating students, breaking tasks into manageable steps, providing guidance, reducing frustration, and modeling expectations. When developing children's books, scaffolding strategies are important to consider by starting with many pictures and few words and gradually increasing the text while decreasing the pictures to guide students from concrete to more abstract understanding as their skills develop.
This document outlines the five core reading skills that are essential for beginning readers: 1) phonemic awareness, 2) phonics, 3) fluency, 4) vocabulary, and 5) comprehension. For each skill, it provides a brief definition and description of how it is developed at different grade levels according to the Sindh Reading Program curriculum. The skills build upon one another to progress from foundational skills like phonemic awareness to higher level skills like comprehension. References are also provided at the end related to each of the five reading skills.
The document discusses decodable texts, which are texts that contain letters and sounds a student has already learned. Decodable texts support early reading instruction by introducing letters and sounds systematically according to a language-specific sequence. To determine if a text is decodable, one considers the sounds a student has learned, the phonetic structure of words using known phonograms, and keeping words short, especially initially focusing on consonant-vowel-consonant patterns. The document requests writing a short decodable story in Urdu/Sindhi and provides references for further information.
The School Improvement Program (SIP) is a systematic effort aimed at improving learning conditions and achieving educational goals more effectively. The SIP uses a decagonal approach involving capacity building for teachers and leadership, community and student participation, improving school environments, enriching curricula, research, and school-based interventions. The goal is to improve school environments and student achievement. Lessons learned include the importance of coordination, using local wisdom, active learning strategies, conducive environments, and recognizing that small improvements are meaningful. Challenges include time for training, staff transfers, perceptions, lack of professionalism, and invisible change processes.
The document discusses feedback and how to effectively give and receive it. It defines feedback as a way to help others change or maintain their behavior by providing information about how their actions affect others. It provides criteria for effective feedback, such as being specific, immediate, descriptive, and behavioral rather than evaluative. The document also gives tips for successfully giving feedback, such as being respectful and focusing on changeable behaviors, and for successfully receiving feedback, like actively listening and seeking continual improvement.
Teacher professional development model where teachers learn best. Comparing learning from Knowledge & Understanding to transfer to classroom repertoire.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
1. A B
CDIn the adjoining figure,
m AE = mEH = a
mEB = mFC = b
mAB = mBC = a + b
Geometrical Proof of formula (a + b)2 = a2 + 2ab + b2
E
F
GK
H
a b
a
b
(a + b)
a2
b2
ab
ab
Area of the square region ABCD =
Area of square region AEHK( a2 )
+ area of the square region HGCF( b2 )
+ area of the rectangular region EBGH( ab )
+ area of the rectangular region KHFD( ab )
i.e. (a+b)2= a2+b2+ab+ab
= a2+2ab+b2
By: Abdul Wasay Yusuf