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