Page 173 - Maths Skills - 8

Mensuration 171

INTRODUCTION
In the earlier classes we have already learnt how to calculate perimeter and area of various plane figures like
rectangle, square, parallelogram, rhombus, triangle etc.
The part of the plane enclosed within a simple closed rectilinear figure is called the region enclosed by it and
the measurement of the region is called its area. A square centimetre or cm is the standard unit of area, which
2
means the area of region enclosed by a square of side 1 cm. Other units of the area are square metre (m ), square
2
decimetre (dm ), square decametre (dam ) etc.
2
2
AREA OF DIFFERENT FIGURES
Area of a Square
The area ‘A’ of a square (Fig.) with all sides of length ‘s’ is given by the formula s

A = s × s
A = s 2 s

Area of a Rectangle
b The area, A, of a rectangle (Fig.) with length ‘l’ and width ‘b’ is given by the

formula A = l × b
l

Area of a Parallelogram h

The area, A, of a parallelogram (Fig.) with height ‘h’ and base ‘b’ is given by the formula
A = base × height/altitude

A = b × h b

Area of a Rhombus
d 1
1
The area, A, of a rhombus (Fig.) with two diagonals d and d is given by A = × d × d
d 1 2 2 1 2
2

Area of a Triangle
The area, A, of a triangle (Fig.) with altitude ‘h’ and base ‘b’ is given by the formula. h
1
A = × base × altitude/height Fact-o-meter b
2
1 Since a rectangle, a square and
A = × b × h a rhombus are parallelogram
2
so the area can be calculated
as a product of base and height
(if both are given).
Area of a Trapezium
As we know, trapezium is a quadrilateral in which one pair of opposite sides is parallel to each other. Let ABCD
be a trapezium with AB and CD as parallel sides measuring ‘a’ and ‘b’ as shown in Fig. Draw a diagonal BD to
divide ABCD into two triangles. Let the distance between the two parallel sides be ‘h’.