This document provides information on mensuration and geometry topics such as trapezoids, rhombuses, cubes, cuboids, cylinders, and their volume and surface area formulas. It includes an introduction to area and surface area concepts. Formulas provided calculate the surface area of a cuboid as 2(lb + bh + hl), a cube as 6l^2, and a cylinder as 2πr(r+h). Volume formulas given are for a cuboid as lxbxh, a cube as l^3, and a cylinder as πr^2h. The document also contains sample problems, diagrams, and a question bank testing knowledge of geometry and volume concepts.

1. MENSURATION

2. Contents
• Introduction
• Trapezium
• Rhombus
• Cube
• Cuboid
• Cylinder
• Table
• Question Bank

3. Introduction
Area of
• a trapezium =half of the sum of the
length of parallel sides x
perpendicular distance between
them.
• a rhombus =half the product of its
diagonals {d1 x d2}
• Surface area of a solid is the sum of
the areas of its faces.

4. Introduction continued…
Surface area of
• a cuboid =2(lb +bh +hl)
• a cube =6l²
• a cylinder =2πr (r+h)
• Volume –amount of region occupied by
a solid is called its volume.

5. Introduction continued…
• Volume of
a cuboid=l x b x h
a cube =l³
a cylinder= πr²h
• 1 cm³=1ml
• 1l=1000 cm²
• 1 m³=1000000 cm³=1000 l

6. TRAPEZIUM
• A trapezium is a quadrilateral whose two
sides are parallel.
• ABCD is a trapezium such that AB and CD
are its two parallel sides while AD and BC are
its non-parallel sides.
• Each of the two parallel sides of b trapezium
is called base of the trapezium.
• The distance between the two bases (parallel
sides) is called the height or altitude of the
trapezium.
• Area of trapezium =half of the sum of the
length of parallel sides x perpendicular
distance between them.
A
D C
B

7. Cube
• A cube is b 3-D figure whose length ,
breadth and height are equal. It has
six faces and all are squares and
identical.
• Surface area of a cube = 6 x (length
of the side)²
• Volume of a cube = (side)³

8. Rhombus
• It is a quadrilateral whose all sides are
equal out of which 2 opposite sides are
parallel and none of the angles are right
angles.
• Area of rhombus=½ x d1 x d2,where d1
and d2 are 2 diagonals

9. CUBOID
• A cuboid is b 3-D figure which has six
rectangular faces and opposite faces
are identical.
• There are three pairs of identical
faces.
• Surface area= 2x(lb + bh +lh)
• Volume= l x b x h

10. Cylinder
• Cylinder is a 3–D figure which has
one curved surface and two circular
faces which are identical.
• Surface area of cylinder= 2πr (r + h)
• Volume of cylinder= πr²h

11. Table
Figure Volume Surface area
Cuboid L x b x h 2(lb +bh +hl)
Cube 6( l )² l³
Cylinder πr²h 2πr (r + h)

12. Question Bank
Multiple-choice Questions
(i) Area of triangle
(a) b x b (c) b x b
(b) ½ x b x h (d) b x a
Ans- ½ x b x h
(ii) If the number of cement bags used to
construct a path is needed, then the
formulae to find the number of cement
bags is -
(a) area of path + area cemented by 1 bag

13. (b) Area of the path x area of place
cemented by 1 bag
(c) Area of the path / area of the
cemented place by 1 bag
(d) none of these
Ans- Area of the path / area of the
cemented place by 1 bag
(iii) What is the area of circle?
(a) b x h (c)πr²

14. (b) l x b (d) all of these
Ans- πr²
(iv) Area of the rhombus-
(a) [area of triangle-1 + triangle-2]
(b) length x breadth (c)½h(a+b)
(d) diagonal 1 x diagonal 2
Ans- diagonal 1 x diagonal 2(v) Volume of a
cylinder is
(a) l x b x h (b)l³ (c)πr²h
(d) None of these
Ans- πr²h

15. (vi) How many centimeters make a litre?
(a)100 cm (b)1000 cm³
(c)both (b) and (a) (d) All of the above
Ans- b)1000 cm³
(vii)How many pairs of faces in cuboids are
identical?
(a) 3 pairs (b) 6 pairs (c) 5 pairs (d) 10
pairs
Ans- 3 pairs
(vii) Perimeter of parallelogram
(a) l x b (b) 2(l + b) (c) 4 x sides (d) None
of these
Ans- None of these

16. (ix) Perimeter of circle
(a) 2(l+b) (b) 3s (c) 2πr (d) 4s
Ans- 2πr
(x) Which are identical parts in cylinder
(a) One curved surface and three circular faces
(b) Two curved surface and one circular face
(c) Both (a) and (b) (d) None of these
Ans- None of these
Correct answer-One curved surface and two
circular faces

17. Short answer type questions
(1) What is triangulation?
Ans- Splitting a quadrilateral into triangles, finding their areas
and hence that of parallelogram
(2) Find the area of a rhombus whose diagonals are of lengths 10
cm and 8.2cm .
Ans- Area of rhombus= d1x d2 where d1,d2 are lengths of
diagonals .
=10 x 8.2 cm² =41 cm²
(3) Find the volume of the cube which has dimensions 2 x 2 x2 cm
Ans- Volume of the cube = 6(l)²
= 6(2)²=6 x 4
= 24 cm³
(4) In which unit is the volume expressed?
Ans- cubic centimeter (cm³)

18. (5)Find the area of quadrilateral PQRS shown in
the figure.
Ans- d=5.5 cm,h1=2.5 cm,h2=1.5 cm
Area=½ d(h1 + h2)
=½ x 5.5 x (2.5+1.5)cm²
=½ x 5.5 x 4 cm²
=11 cm²
P
S
R
Q
1.5
5.5 2.5

19. THANK
YOU