A parallelogram has sides 60 m and 40m and one of its diagonals

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A parallelogram has sides 60 m and 40m and one of its diagonals is 80 m long. Its area is

1. 500√15 m²
2. 600√15 m²
3. 400√15 m²
4. 450√15 m²

Correct Option: B

Using Rule 1,

Semiperimeter of ∆ABC(s) =	a + b + c
	2

=	60 + 40 + 80	= 90 metre
	2

∴ Area of ∆ABC = √s(s - a)(s - b)(s - c)
= √90 (90 – 60) (90 – 40) (90 – 80)
= √90 × 30 × 50 × 10
= √3 × 30 × 30 × 5 × 10 × 10
= 30 × 10√15
= 300√15 sq. metre
∴ Area ∎ of ABCD
= 2 × Area of ∆ABC
= 2 × 300√15
= 600√15 sq. metre