Q19. - Geometry

Question

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

Step-by-Step Solution

Answer

Area of the figure  $\left(A\right)=48sq.units$

Step 1. Given information.

Consecutive sides of the figure is perpendicular.

   Hypotenuse of the triangles $H=10$

             Base of the triangles  $B=8$

Step 2. Concept Used.

Since the two triangles are right angles triangles.

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

Using the Pythagoras theorem-

$H^2=B^2+P^2$

Step 3. Let’s calculate the height of the figure.

$\begin{array}{l}{H}^2=B^2+P^2\\ {10}^2=8^2+P^2\\ P^2=100-64\\ P^2=36\\ P=6units\end{array}$

Now,  area of the triangle

$\begin{array}{c}A=\frac{1}{2}(b\times h)\\ =\frac{1}{2}(8\times 6)\\ =24sq.units\end{array}$

 

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

Thus,  $\begin{array}{c}A=\left(2\right)\times 24\\ =48sq.units\end{array}$

 

Therefore, the area of the figure $\left(A\right)=48sq.units$