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Question

A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long.
The area of the parallelogram is 600k m2. Find the value of k

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Solution

From above figure,
Quadrilateral ABCD is a parallelogram, with sides AB=CD=60m,BC=DA=40m and diagonal BD=80m
Area of parallelogram ABCD=2× (Area of ABD)
In ABD,
Semi-perimeter of ABD,
s=a+b+c2
AB+BD+DA2
60+80+402
1802
90m
So, by Heron's formula,
Area of ABD = s(sa)(sb)(sc)

90(9060)(9080)(9040)
90×30×10×50
100×315m2
So, area of parallelogram ABCD=2×30015=60015m2
The value of k is 15.

811324_78125_ans_5c39722c241b4a5ca2012b02053b969a.png

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