Question:
two adjacent sides of a parallelogram are 74 cm and 40 cm. if one of its diagonals is 102 cm then would be the area of parallelogram
Answer:
Let the two adjacent sides of the parallelogram be a = 74 cm, b = 40 cm
Let the length of diagonal be c = 102 cm
These two sides and the diagonal forms a triangle
semi perimeter, s = (a + b + c)/2
s = (74 + 40 + 102)/2 = 216/2 = 108 cm
By Heron formula, we have area of triangle, Δ = √[s(s - a)(s - b)(s - c)]
= √[108(108 - 74)(108 - 40)(108 - 102)]
= √{108 * 34 * 68 * 6}
= √{3 * 4 * 9 * 34 * 2 * 34 * 6}
= √{3 * 4 * 9 * 34 * 2 * 34 * 6}
= √{6 * 4 * 9 * 34 * 34 * 6}
= 6 * 2 * 3 * 34
= 1224 sq cm
Area of parallelogram = 2 * area of triangle = 2 * 1224 = 2448 sq cm
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