Question

A parallelogram has sides 15 cm and 7 cm long. the length of one of the diagonals is 20cm. the area of the parallelogram is

Answer 1

Area of parallelogram of sides a, b and one diagonal c =

$A = 2\sqrt{s(s - a)(s - b)(s - c)} \\ \\ s = \frac{a + b + c}{2}$

Here,

a = 15 cm

b = 7 cm

c = 20 cm

$s = \frac{15 + 7 + 20}{2} = \frac{42}{2} = 21 \\ \\ \\ A = 2\sqrt{21(21 - 15)(21 - 7)(21 - 20)} \\ \\ = 2\sqrt{21 \times 6 \times 14 \times 1} \\ \\ = 2\sqrt{7 \times 3 \times 3 \times 2 \times 2 \times 7} \\ \\ = 2 \times 7 \times 3 \times 2 = 84 cm^2$

84 cm² is the answer.

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Answer 2

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