Area and Perimeter

Perimeter

Perimeter means distance around a figure or curve. We can only measure perimeter of a closed figure/2 dimensional shape or curve as movement around a closed figure or curve is possible.

Perimeter of a Square

A square is a closed figure that has 4 sides of equal length and 4 equal angles of 90 degree.

Perimeter of a square

= sum of all sides

OR                               

= 4 x side

Perimeter of a Rectangle

A rectangle is a closed figure that has equal opposite sides and each angle is of 90 degree. The longer side of rectangle is known as length of the rectangle and shorter side is known as width or breadth of rectangle.

Perimeter of Rectangle

= L + L + B + B

OR

= 2 X L + 2 X B (i.e. 2L + 2B)

OR

= 2 (L + B) (taking 2 common i.e. twice the sum of length and breadth)

Perimeter of a Triangle

A triangle is a plane figure with three straight sides and three angles.

Perimeter of Triangle

= S + S + S

OR

= Sum of lengths of three sides

Area

Area is the space enclosed by a plane figure (2 Dimensional shapes).

Area is measured in "square" units. The area of a plane figure is the number of squares needed to cover it completely.

Area of Square

Area of square is equal to the product of its length and breadth expressed in square units. But, in case of square length and breadth are same, we express area by multiplying its side and side.

Area of Square = Side x Side

Area of Rectangle

Area of rectangle is equal to the product of its length and breadth expressed in square units.

Area of Rectangle = Length x Breadth

Area of Irregular shapes

To calculate the area of irregular figure, first we have to divide irregular figure into regular recognizable shapes such as square, rectangle etc. and then add the area of all the shapes.

To find the cost of painting or tiling

Step 1: Find the area.

Step 2: Multiply the area with cost of painting or tiling per sq. unit

Cost of painting or tiling = area x cost per sq. unit

Illustration: Find the cost of painting a wall of a length 30 m and breadth 10 m at the rate of rupees 10 per sq. m.

Solution:

Area of wall = l x b = 30 x 10 = 300 sq. m

Cost of painting = area x cost per sq. m = 300 x 10 = Rs.3000

To find the number of bricks or tiles

Step 1: Find area of wall or floor.

Step 2: Find area of bricks or tiles

Step 3: Divide area of wall or floor by area of a brick or a tile

Number of brick or tile = Area of wall or floor/Area of a tile or a brick

Illustration: Find the number of bricks to be laid in a square path of side 1 m, if the side of each square brick is 5 cm.

Solution:

1 m = 100 cm

Area of square path = 100 cm x 100 cm

Area of brick = 5 cm x 5 cm

Number of bricks required

  = 400