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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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