What is Mensuration? We all come across various shapes in our life which includes rectangles, squares, triangles and a lot more. But a very important question arises that how do we measure these shapes? What are their length, width and height and what area do they occupy? Here we are going to learn about the measurements of these various shapes.

Mensuration is basically nothing but the measurements of the dimensions, areas and various other parameters of any closed or open figure. Perimeter

Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once.

Perimeter has a great physical application which includes like

• Calculated perimeter is the length of fence required to surround garden or park.
• The perimeter of a wheel called as circumference describes how far it will roll in one revolution.
• The amount of string wound around a spool is related to the spool's perimeter.

Perimeter of a Rectangle Example 1: Find the perimeter of a regular pentagon whose side length is 5 cm.

Solution: No. of sides = 5

Length of each side = 5 cm.

Perimeter = 5+5+5+5+5 or 5 x 5 = 25 cm.

Hence the perimeter comes out to be 25 cm.

Perimeter of Square

= 4 x (Side of Square) Example 2: The perimeter of a square park is 20 cm. If it’s one side has to be fenced by a wire again, then find out the cost needed at a rate of Rs 4/cm.

Solution: Perimeter of Square = 20 cm = 4 x (Side of Square)

And from here we get side of square = 20cm / 4 = 5cm.

Hence the length of side required to be fenced = 5cm

Rate = Rs 4/cm

Therefore total cost = 5 x Rs 4 = Rs 20.

Perimeter of Triangle

3 x length of a side Area

The amount of surface enclosed by a closed figure is called it’s area.

Area of Square = (Length of side)2

Area of Rectangle = Length x Breadth Practice Questions

Q1) Find the perimeter of a rectangle of length 12 cm and breadth 10 cm.

Q2) If the perimeter of a triangle is 72 cm. Find the length of the side of the triangle.

Q3) Find the area and perimeter of a square of side 8 cm.

Q4) If the area of a rectangle is 20 cm2 and the perimeter is 18 cm. Then find the length and breadth of the rectangle.

Q5) A room has a dimension of 40cm x 20cm. If the rate of tiling the floor is Rs 100/cm2, then find the cost of tiling the floor.

Recap

• Perimeter is the distance covered along the boundary when you go round the boundary once.

• Perimeter of a rectangle = 2 × (length + breadth)
• Perimeter of a square = 4 × length of its side
• Perimeter of an equilateral triangle = 3 × length of a side

• The amount of surface enclosed by a closed figure is called its area.

• Area of a rectangle = length × breadth
• Area of a square = side × side

The figures in which all sides and angles are equal are called regular closed figures.