This document provides information about calculating the areas and volumes of various geometric shapes and solids. It includes formulas for finding the area of rectangles, squares, triangles, circles, parallelograms, trapezoids, rhombuses, as well as the surface area and volume of cubes, cuboids, cylinders. Specific details are provided on the geometric properties of trapezoids, rhombuses, cubes, cuboids and cylinders. Formulas for calculating their surface areas and volumes are defined. A table at the end summarizes the volume and surface area formulas for cuboids, cubes and cylinders.

1. MENSURATION

2. Contents
Area of geomentrical shapes
Mensuration
Introduction
Volume
Trapezium
Rhombus
Cube
Cuboid
Cylinder
Table

3. Areas of geometrical shapes
Diagram Shape Area
RECTANG
LE
L x W
SQUARE
a x a
TRIANGL
E
1/2xbxh

4. CIRCLE πr²
PARALLELOGR
AM
B x h
TRAPEZIUM ½(a+b)
h

5. Mensuration
To find perimeter or
area of a plane is known
as Mensuration

6. Introduction
Area of trapezium: half of the sum of the length
Of parallel sides x perpendicular distance between them.
Area of a rhombus: half the product of its diagonals
{d1xd2}.
Surface area of a solid is the sum of the areas
Of its faces.

7. Surface area of a cube: 61²
Surface area of a cuboid: 2(lb+bh+hl)
Surface area of a cylinder: 2πr(r+h)
VOLUME
Amount of region occupied by a
solid is called its volume.
Volume of a cuboid: lxbxh
Volume of a cube: l3
Volume of a cylinder: πr²h

8. 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. D A C B

9. 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

10. 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

11. 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

12. 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

13. Table
shape volume Surface
area
cuboid lxbxh 2(lb+bh+hl)
cube 6(l)² l³
cylinder πr²h 2πr(r+h)

14. Prepared by
G.SRI HARSHA
VIII D