1.

Find the area of a parallelogram with a diagonal of length 8 cm and having adjacent sides of 4 cm and 6 cm.1). 11.6 cm22). 16.4 cm23). 20.1 cm24). 23.2 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 = 8 CM, b = 4 cm, c = 6 cm, we get,

s = (8 + 4 + 6)/2 = 18/2 = 9

∴ Area of parallelogram = 2 × √9(9 – 8)(9 – 4)(9 – 6) = 2 × √135 = 2 × 11.6 = 23.2 cm2


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