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

Question

Philoid · Accepted Answer

For Area(ΔBCD),

a = 60, b = 40, c = 80

s = (a + b + c)/2

⇒ s = (60 + 40 + 80)/2 = 180/2 = 90.

Area(ΔBCD) = √s(s-a)(s-b)(s-c)

⇒ Area(ΔBCD) = √90(90-60)(90-40)(90-80)

⇒ Area(ΔBCD) = √90×30×50×10

⇒ Area(ΔBCD) = 300√15 cm²

As ABCD is a parallelogram, Area(ΔBCD) = Area(ΔABD)

⇒ Area of parallelogram(ABCD) = Area(ΔBCD) + Area(ΔABD)

⇒ Area of parallelogram(ABCD) = 300√15 + 300√15

⇒ Area of parallelogram(ABCD) = 600√15 = 2323.79 cm²