Question

A garden is in the shape of a rhombus with side 35 m and one diagonal 42 m. Find its area.

• A. 2442 sq. m
• B. 1296 sq. m
• C. 1176 sq. m
• D. 1024 sq. m

Answer 1

The correct option is C 1176 sq. m

Let ABCD be the garden
Side, DC = 35 m
Diagonal, DB = 42 m
We know that the diagonals of a rhombus bisect each other at right angles.
Therefore,
DE = 1/2×42 = 21 m
In right-angled triangle DEC, applying pythagoras,
CD² = CE² + DE²
CE² = CD² - DE² = 35² - 21²
CE² = 784
CE = 28 m
Now,
Area of △DBC = 1/2×DB×CE
= 1/2×42×28
= 588 m²
Therefore,
Area of the garden ABCD = 2×588
= 1176 m²