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?
Draw a rhombus-shaped field first with the vertices as ABCD. The diagonal AC divides the rhombus into two congruent triangles which are having equal areas. The diagram is as follows.
Consider the triangle BCD,
Its semi-perimeter
= \(\frac{48+ 30+30}{2}\)
= 54 m
Using Heron’s formula,
Area of the ΔBCD
= \(\sqrt{s(s - a)(s - b)(s - c)}\)
= \(\sqrt{54(54 - 48)(54 - 30)(54 - 30)}\)m2
= \(\sqrt{54 \times 6 \times 24 \times 24}\)m2
= 432 m2
∴ Area of field = 2 × area of the ΔBCD
= (2 × 432) m2 = 864 m2
Thus, the area of the grass field that each cow will be getting
= (864/18) m2 = 48 m2