CBSE Class 7 Mathematics Perimeter And Area Notes

Perimeter and Area

11.1 Perimeter

A perimeter is a path that surrounds an area. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circular area is called circumference.

11.2  Area

Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane.

11.3  Formulae to Find Area and Perimeter

Square

If ‘a’ is the length of side of a square, then its      

i) Perimeter, P = 4 x a units

ii)Area, A = a² square units

Note:

1.If perimeter ‘P’ of a square is given, then its side, a = P/4 units

2. If area ‘A’ of a square is given, then its side, a = Square root of A

Rectangle

If ‘l’ is the length and ‘b’ is the breadth of a rectangle, then its

i) Perimeter , P= 2 x ( l + b )  units

ii) Area, A = l x b square units

Note

i) If perimeter ‘P’ and length ‘l’ of a rectangle are given, then its breadth, b = (P/2) – l units

ii) If perimeter ‘P’ and breadth ‘l’ of a rectangle are given, then its length, l = (P/2) – b units

iii)  If area ‘A’ and length ‘l’ of a rectangle are given, then its breadth, b = (A/l)

iv) If area ‘A’ and breadth ‘l’ of a rectangle are given, then its length, l = (A/b)

Generalising For Other Congruent Parts of Rectangles

 If a rectangle is composed of ‘n’ number of congruent polygons, then area of each polygon = (Area of rectangle/ n)

Note:

If area of one congruent polygon is given, then area of rectangle composed of n congruent polygon = area of each polygon x n

Parallelogram

If ‘b’ is the base and ‘h’ is the height of a parallelogram then its area,     

A = b x h sq. units   

Note:

i) If area ‘A’ and base ‘b’ of a parallelogram are given, then its height h, h = (A/b)

ii) If area ‘A’ and height ‘h’ of a parallelogram are given, then its base b = (A/h)

Triangle

If 'b' is the  base  and 'h' is the height of  a triangle then its area,

Note:

i) All the congruent triangles are equal in area but the triangles equal in area need not be congruent.

ii) If area ‘A’ and base ‘b’ of a triangle are given, then its height h, h = (2A/b)

iii)  If area ‘A’ and height ‘h’ of a triangle are given, then its base b = (2A/h)

Circle

If r is the radius of the circle, then its

Circumference, C = π d = π × 2r units

 ii)Area, A  = π r² square units