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Question
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?
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Solution
Let ABCD be a rhombus-shaped field.
For ΔBCD,
Semi-perimeter,
`s=(48+30+30)/2 = 54 m`
By Heron's Formula,
`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`
`therefore" Area of ΔBCD "=[sqrt(54(54-48)(54-30)(54-30))]m^2`
`=sqrt(54(6)(24)(24))`
= 3 x 6 x 24
= 432 m2
Area of field = 2 × Area of ΔBCD
= (2 × 432) m2 = 864 m2
Area for grazing for 1 cow = 864/18 = 48 m2
Each cow will get 48 m2 area of grass field.
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