The area of the parallelogram whose length is 30 cm, width

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The area of the parallelogram whose length is 30 cm, width is 20 cm and one diagonal is 40 cmis

1. 200√15 cm²
2. 100√15 cm²
3. 300√15 cm²
4. 150√15 cm²

Correct Option: D

Using Rule 1,

In ∆ABD,
AB = 20 cm. AD = 30 cm. BD = 40 cm.

∴ Semi–Perimeter (s) =	a + b + c	=	20 + 30 + 40
	2		2

= 45 cm
∴ Area of ∆ABD
= √s(s - a)(s - b)(s - c)
= √45(45 - 20)(45 - 30)(45 - 40)
= √ 45 × 25 × 15 7times; 5
= √5 × 3 × 5 × 5 × 5 × 3 × 5
= = √5² × 5² × 5 × 3² × 3
= 5 × 5 × 3√15 = 75√15 square cm.
∴ Area of parallelogram ABCD = 2 × 75√15
= 150√15 square cm.