Question

the floor of a room is in shape of parallelogram which its adjacent sides are 51m and 37m. one of its diagonals is 20 m. find area of room and altitide.

Answer 1

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) / 2s = (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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