# A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

**Solution:**

We will divide the given rhombus into two triangles, and by using Heron’s formula, we can calculate the area of triangles.

Heron formula for the area of a triangle = √s(s - a)(s - b)(s - c)

Where a, b and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2

Let the longer diagonal AC divides the rhombus ABCD into two congruent triangles.

For ∆ABC, a = b = 30 m, c = 48 m

And Semi Perimeter(s) = (a + b + c)/2

s = (30 + 30 + 48)/2

s = 108/2

s = 54 m

By using Heron’s formula,

Area of ΔABC = √s(s - a)(s - b)(s - c)

= √54(54 - 30)(54 - 30)(54 - 48)

= √54 × 24 × 24 × 6

Area of ΔABC = 432 m^{2}

Area of rhombus = 2 × Area of a ΔABC

= 2 × 432 m^{2}

= 864 m^{2}

Since, number of cows = 18

The area of grass field will each cow get = (Total area of the rhombus) / 18

= 864 m^{2}/18

= 48 m^{2}

Thus, each cow will be getting a 48 m^{2} area of the grass field.

**Video Solution:**

## A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

### Class 9 Maths NCERT Solutions - Chapter 12 Exercise 12.2 Question 5:

**Summary:**

It is given that rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, we have found that each cow would be getting an area of 48 m² to graze.