Two adjacent sides of a parallelogram are 21 cms and 20

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Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq. cms) is

1. 240
2. 120
3. 210
4. 420

Correct Option: D

Area of parallelogram ABCD = 2 × Area of ∆ABC
AB = 21 cm. = c
BC = 20 cm. = a
AC = 29 cm. = b

∴ Semi-perimeter of ∆ABC = s =	a + b + c
	2

=		20 + 29 + 21		cm.
		2

=	70	= 35 cm.
	2

∴ Area of ∆ABC
= √8(s – a)(s – b)(s – c)
= √35(35 – 20)(35 – 29)(35 – 21)
= √35 × 15 × 6 × 14
= √7 × 5 × 5 × 3 × 2 × 3 × 2 × 7
= 7 × 2 × 3 × 5 = 210 sq.cm.
∴ Area of ABCD = (2 × 210) sq. cm.
= 420 sq. cm.