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Question

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


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Solution

Given

ABCD is a rhombus having diagonal AC

side AB=BC=CD=AD=30cm

The diagonal of the Rhombus divides the area into two equal parts.

Find out

We have to determine how much area of grass field will each cow be getting

Solution

Using Heron’s formula, area of the triangle =ss-as-bs-c

Now, arABC can be calculated by Heron’s Formula, where

AB = a =30cm

BC =b=30cm

AC = c =48cm

Semi Perimeter s=a+b+c2

s=30+30+482s=1082s=54m

arABC =ss-as-bs-c

=5454-3054-3054-48=54×24×24×6=432m2

Hence, the Area of rhombus =2×arABC

=2×432=864m2

Area for 18 cows =864m2

Area for each cow = 86418=48m2

Therefore, area for each cow 48m2.


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