Question 71

Find the area of a rhombus, one of its sides being 25 cm and one of the diagonals being 30 cm.

Solution

let diagonal CA = 30 cm

CA = OA + OC = 15 + 15 = 30

from triangle OCB

$$ BC^2 = OB^2 + OC^2 $$

$$ 25^2 = OB^2 + 15^2 $$

$$ 625 = OB^2 + 225 $$

$$ OB^2 = 400 $$

0B = 20

DB = OD + OB = 20 + 20 = 40

area of rhombus = $$ \frac{1}{2} d1 d2 $$

= $$ \frac{1}{2} \times 30 \times 20 $$

= $$ 600 cm^2 $$

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