Mensuration Formula – 2D and 3D shapes

Mensuration Formula (2D and 3D shapes)

Definition:

Mensuration is the part of mathematics that deals with the length, area, and volume of different geometrical figures.

Type of shapes and differences:

The two things that are broadly dealt with in Mensuration are two-dimensional figures and three-dimensional solids. The detailed description, along with their differences, is attached below:

Important terms:

2D mensuration formula:

Mensuration formula 3D:

Solved Examples:

1. Calculate the area of a square with side 5 cm.

The area of a square of side 5cm is A=L^{2}=5^{2}=25 \mathrm{~cm}^{2}

2. Calculate the perimeter of a rectangle having a length of 10 cm and breadth of 5 cm.

The perimeter of a rectangle with length 10 cm and breadth 5 cm is 2( l + b) = 2(10 + 5) = 30 cm.

3. What is the area of a right-angled triangle with two of its perpendicular sides as 3 and 4 cm?

The area of a right angled triangle with two of its perpendicular sides as 3 cm and 4 cm is:

A = ½ x b x h = 0.5 x 3 x 4 = 6 \mathrm{~cm}^{2}.

4. Calculate the volume of a cone having a radius of 7 cm and height of 5 cm?

The volume of a cone with a radius of 7 cm and height of 5 cm is:

(1 / 3) \pi r^{2} h=256.67 \mathrm{~cm}^{3}

5. What is the total surface area and curved surface area of a cylinder with a radius of 14 cm and height of 10 cm?

The total surface area of a cylinder with radius 14 cm and height 10 cm is:

2 \pi r h+2 \pi r^{2}=2112 \mathrm{~cm}^{2}

The curved surface area of a cylinder with radius 14cm and height 10cm is:

2 \pi r h=880 \mathrm{~cm}^{2}