1.

Find the area of a parallelogram with a diagonal of length 10 cm and having adjacent sides of 8 cm and 6 cm.1). 41.6 cm22). 44 cm23). 24 cm24). 48 cm2

Answer»

As we KNOW, the diagonal of a parallelogram divides it into two EQUAL triangles.

Hence,

Area of parallelogram = 2 × area of triangle FORMED by the two adjacent sides and the diagonal

⇒ Area of parallelogram = 2 × √s(s – a)(s – b)(s – c)

Where s = (a + b + c)/2

Putting a = 10 cm, b = 8 cm, c = 6 cm, we get,

s = (10 + 8 + 6)/2 = 24/2 = 12

⇒ Area of parallelogram = 2 × √[12(12 – 10)(12 – 8)(12 – 6)] = 2 × √576 = 2 × 24 = 48 cm2


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