1. The document provides examples of calculating the areas of various shapes, including circles, rectangles, triangles, trapezoids, parallelograms, and composite figures.
2. It gives the formulas for calculating the areas of these shapes and shows step-by-step workings for multi-part composite figures and shaded regions.
3. The examples are meant to demonstrate how measurements can be used to describe real-world objects and areas.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
1. Find the area of each circle. Round to the nearest tenth. Use 3.14
or for .
1. 2.
3. 4.
5. Rick wants to make a big cookie cake. If he uses a round cookie
sheet that is 12 inches in diameter, about how much cookie dough
will he need to cover the pan?
22
7
Course 2, Lesson 8-3
8. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Find the area of the
composite figure.
The figure can be separated into
a semicircle and a triangle.
Area of semicircle
The area of the figure is about 14.1 + 33 or 47.1
square meters.
Area of triangle
A = πr2
A ≈ • 3.14 • 32
A ≈ 14.1
A = bh
A ≈ • 11 • 6
A ≈ 33
10. 1
Need Another Example?
2
3
Step-by-Step Example
2. A miniature golf hole is
composed of a trapezoid
and a parallelogram. How
many square feet of turf
does the hole cover?
Area of trapezoid
So, 7.5 + 15 or 22.5 square feet of turf will be needed.
Area of parallelogram
A = h(b1 + b2)
A = (3)(2 + 3)
A = 7.5
A = bh
A = 6 • 2.5
A =15
11. Answer
Need Another Example?
The back of a dog house is composed of a square and
a triangle. How much wood is needed for the back of
the dog house to the nearest tenth of a square foot?
8.1 ft2
12. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. Find the area of the
shaded region.
Area of rectangle
The area of the shaded region is 60 – 2 or
58 square inches.
Area of triangles
Find the area of the rectangle and
subtract the area of the four triangles.
ℓ = 12, w = 5
b = 1, h = 1
Simplify.
Simplify.
A = ℓw
A = 12 • 5
A = 60
A = 4 • bh
A = 4 • • 1 • 1
A = 2
13. Answer
Need Another Example?
Two congruent triangles are cut from a rectangle.
Find the area of the shaded region. Round to the
nearest tenth if necessary.
144 in2
14. 1
Need Another Example?
2
3
Step-by-Step Example
4. The blueprint for a hotel
swimming area is
represented by the figure
shown. The shaded area
represents the pool. Find
the area of the pool.
Area of the entire rectangle
Find the area of the entire rectangle and subtract the
section that is not shaded.
Area not shaded
The area of the shaded region is 1,050 – 440 or
610 square meters.
A = ℓw
A = 42 • 25 or 1,050
A = ℓw
A = 22 • 20 or 440
15. Answer
Need Another Example?
Mario sketched a drawing of a dirt bike track he wants his dad to
build. The brown area represents the track. Find the area of the
track. Round to the nearest tenth.
2,590.5 ft2
16. How did what you learned
today help you answer the
Course 2, Lesson 8-3
Geometry
HOW do measurements help you
describe real-world objects?
17. How did what you learned
today help you answer the
Course 2, Lesson 8-3
Geometry
HOW do measurements help you
describe real-world objects?
Sample answers:
• To find the area of a composite figure, such as a
miniature golf course hole
• To find the area of the shaded portion of a figure, such
as the blueprint of a swimming pool area
18. What measurements would
you need to know in order to
find the area of the figure at
the right? What steps would
you take to find its area?
Course 2, Lesson 8-3
Ratios and Proportional RelationshipsFunctionsGeometry
