Q20. - Geometry

Question

Consecutive sides of the figures are perpendicular. Find the area of each figure. 

Step-by-Step Solution

Answer

Area of the figure   $\left(A\right)=81\sqrt{3}units$

Step 1. Given information.

Consecutive sides of the figure is perpendicular.

Step 2. Concept Used.

Since the two triangles are right angles triangle.

 Where, B  is the base of the triangles P ,  is the height of the triangles and H  is the Hypotenuse of the triangles.

Each triangle is ${30}^0-{60}^0-{90}^0$  triangle. 

Then

 sides follow the ratio 

   $1:\sqrt{3}:2$

Thus- 

 $\begin{array}{l}H=18units\\ B=\frac{18}{2}=9units\\ P=9\sqrt{3}units\end{array}$

Step 3. Let’s calculate the area of the triangle.

Now,  area of the triangle

 

 $\begin{array}{c}A=\frac{1}{2}(B\times P)\\ =\frac{1}{2}\left(9\right)\times \left(9\sqrt{3}\right)\\ =\frac{81\sqrt{3}}{2}\end{array}$

We know that the diagonal of a rectangle divide it into two equal triangles.

Thus,  

 $\begin{array}{c}A=\left(2\right)\times \frac{81\sqrt{3}}{2}\\ =81\sqrt{3}units\end{array}$

 

Therefore, the area of the figure  $\left(A\right)=81\sqrt{3}units$