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 grazing?

If a triangle has three sides, a, b, and c, semi-perimeter s, and the area of triangle A, then the semi-perimeter and area of the triangle are given as:

$\mathrm{s}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$

$\text{A}=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$

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) = $\frac{(\mathrm{a} + \mathrm{b} +\mathrm{c})}{2}$

s = $\frac{(30 + 30 +48)}{2}$

s = $\frac{108}{2}$

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 m²

Area of rhombus = 2 × Area of a ΔABC

                               = 2 × 432 m² = 864 m²

Since the number of cows = 18

The area of grass field each cow will get = $\frac{\mathrm{Total} \mathrm{area} \mathrm{of} \mathrm{the} \mathrm{rhombus} }{18}$

            $= \frac{864 {\mathrm{m}}^2}{18} = 48 {\mathrm{m}}^2$

Thus, each cow will be getting a 48 m² area of the grass field.