Q19 of 84 Page 114

Find the area of the rhombus ABCD with vertices A (2, 0), B (5, –5), C (8, 0) and D (5, 5). [Hint: Area of the rhombus ABCD = 1/2d1 d2]

Formula used:


Coordinates of rhombus are A (2, 0), B (5, –5), C (8, 0) and D (5, 5)


Area of rhombus =


Distance of AC(d1)


⇒ AC = √ ((8 – 2)2 + (0 – 0)2)


⇒ AC = √ ((6)2 + (0)2)


⇒ AC = √ (36 + 0)


⇒ AC = √ 36


⇒ AC = 6


Distance of BD(d2)


⇒ BD = √ ((5 – 5)2 + (5 – (–5))2)


⇒ BD = √ ((5 – 5)2 + (5 + 5)2)


⇒ BD = √ ((0)2 + (10)2)


⇒ BD = √ (0 + 100)


⇒ BD = √ 100


⇒ BD = 10


∴ Area of rhombus =


⇒ Area


⇒ Area = 3 × 10


⇒ Area = 30 units sq.


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