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Grade 99 grade maths

The length of the adjacent side of a parallelogram are 37 and 51 cm respectively and the length of one it’s of its diagonal is 20 cm find the area of the parallelogram

Profile image of vivek BONAGIRI
8 Years agoGrade 9
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1 Answer

Profile image of Arun
8 Years ago
Let the two adjacent sides of the parallelogram be a = 51 cm, b = 37 cm
Let the length of diagonal be c = 20 cm
These two sides and the diagonal forms a triangle
semi perimeter, s = (a + b + c) / 2
s = (51 + 37 + 20)/2 = 54 cm
By Heron's formula, we have area of triangle, Δ = √s(s - a)(s - b)(s - c)
= √[54(54 - 51)(54 - 37)(54 - 20)
= √54 x 3 x 17 x 34
= 306 sq cm
Area of parallelogram = 2 x area of triangle = 2 x 306 = 612 sq cm

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