Q34. - Geometry

Question

The diagonals of a rectangle are18cm long and intersect at a$$" width="9" height="19" style="max-width: none; vertical-align: -4px;" >${60}^{\circ }$ angle. Find the area of the triangle.

Step-by-Step Solution

Answer

The area of the triangle is$81\sqrt{3}c{m}^2$ .

Step 1. Given information.

The diagonal of a rectangle are18cm long and intersect at${60}^{\circ }$ angle.

Step 2. Concept Used.

The area of the rectangle is 
$A=length\times breadth$

Step 3. Let’s calculate the area of each square and the value of s.

The diagonal of a rectangle are18cm long.

i.e $AC=BD=18cm$

We know that the diagonals of a rectangle bisect each other.

Thus $\begin{array}{l}A=lb\\ A=\left(9\sqrt{3}\right)\left(9\right)\\ A=81\sqrt{3}c{m}^2\end{array}$