A rhombusshaped 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?
A rhombusshaped 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 rhombusshaped 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 semiperimeter
= \(\frac{48+ 30+30}{2}\)
= 54 m
Using Heron’s formula,
Area of the ΔBCD
= \(\sqrt{s(s  a)(s  b)(s  c)}\)
= \(\sqrt{54(54  48)(54  30)(54  30)}\)m^{2}
= \(\sqrt{54 \times 6 \times 24 \times 24}\)m^{2}
= 432 m^{2}
∴ Area of field = 2 × area of the ΔBCD
= (2 × 432) m^{2 }= 864 m^{2}
Thus, the area of the grass field that each cow will be getting
= (864/18) m^{2 }= 48 m^{2}

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