Introduction:

Mensuration deals with length, area and volume of different kinds of shape- both 2D and 3D.  It is based on the use of algebraic equations and geometric calculations to provide measurement data regarding  the width, depth and volume of a given object or group of objects. While the measurement results obtained by the use of mensuration are estimates rather than actual physical measurements, the

calculations are usually considered very accurate.

There are two types of geometric shapes: 2D and 3D

 2D shapes are: Square, Rectangle, Parallelogram, Rhombus, Triangle, Trapezoid, Circle

3D shapes: They have surface area and volume.

Cube, Cuboids, Cylinder, Cone, Sphere, Prism, Pyramid.

Problem: A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Solution:

Given: The side of a square = 60 m

And the length of rectangular field = 80 m

According to question,

Perimeter of rectangular field = Perimeter of square field

=> 2(l + b) = 4 * side

=> 2(80 + b) = 4 * 60

=> 160 + 2b = 240

=> 2b = 240 – 160

=> 2b = 80

=> b = 80/2

=> b = 40

Now, Area of Square field = (side)² = (60)² = 60 * 60 = 3600 m²

And Area of Rectangular field = length * breadth = 80 * 40 = 3200 m²

Hence, area of square field is larger.