Question

A rhombus has its side equal to 17 cm and one of its diagonals equal to 16 cm. Find the area of the rhombus.

• A. 240 cm²
• B. 120 cm²
• C. 256 cm²
• D. None of the above

Answer 1

The correct option is A 240 cm²


In a rhombus, all the sides are equal and the diagonals bisect each other.
$\text{Area of Rhombus}=\frac{1}{2}\times \text{Product of diagonals}=AC\times BD$
Given, AD = 17 cm; AC = 16 cm
So, OA = OC = $\frac{AC}{2}=\frac{16}{2}=8cm$

We know that $AO\perp OD$ $\because \text{Diagonal will be perpendicular to each other}$
So, In △AOD
$A{D}^2=A{O}^2+O{D}^2$
$\Rightarrow {17}^2=8^2+O{D}^2$
$O{D}^2=289-64=225$
$\Rightarrow OD=\sqrt{225}$
$OD=15cm$
So, $BD=2\times OD=30cm$

Area of rhombus ABCD = $\frac{1}{2}\times AC\times BD=\frac{1}{2}\times 30\times 16=15\times 16=240c{m}^2$