Question

find the area of a parallelogram whose adjacent sides are 50cm and 60cm and one of the diagonal is 70cm ?

Answer 1

Hey mate
I would use Heron’s formula, and then double the result. I don’t know of a more elegant way. Usually the area of a parallelogram is determined using the height, but your question gives the diagonal, not the height or altitude.

Answer 2

Answer:

2939.38 cm²

Step-by-step explanation:

Given adjacent sides are 50 cm and 60 cm, Diagonal = 70 cm.

Let a = 50 cm, b = 60 cm, c = 70 cm.

Area of ΔABC:

∴ s = (a + b + c)/2

     = (50 + 60 + 70)/2

     = 90.

∴ar(ABC) = √s(s - a)(s - b)(s - c)

               = √90(90 - 50)(90 - 60)(90 - 70)

               = √90(40)(30)(20)

               = √2160000

               = 1469.69

∴Ar(ABCD) = 2 * ar(ABC)

                  = 2 * 1469.69

                  = 2939.38 cm².

Hope it helps!