MENSURATION

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

Areas of geometrical shapes

Diagram Shape Area

RECTANGLE

L x W

SQUARE a x a

TRIANGLE

1/2xbxh

CIRCLE πr²

PARALLELOGRAM

B x h

TRAPEZIUM ½(a+b)h

Mensuration

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

Introduction Area of trapezium: half of the sum of the lengthOf 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 areasOf its faces.

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

TRAPEZIUMA 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

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

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

CUBOIDA 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

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

Tableshape volume Surface

areacuboid lxbxh 2(lb+bh+

hl)cube 6(l)² l³

cylinder πr²h 2πr(r+h)

Prepared by G.SRI HARSHA VIII D