Q22. - Geometry

Question

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

Step-by-Step Solution

Answer

Area of the figure   $\left(A\right)=\frac{49}{2}sq.units$

Step 1. Given information.

Consecutive sides of the figure is perpendicular.

Step 2. Concept Used.

Where, b  is the base of the triangles ,i  is the height of the triangles and H  is the Hypotenuse of the triangles. 

$△ABC$  is-  $({45}^0+{45}^0+{90}^0)$

Thus,$\begin{array}{l}\mathrm{Cos}{45}^0=\frac{b}{H}\\ \frac{1}{\sqrt{2}}=\frac{b}{H}\\ b=\frac{H}{\sqrt{2}}\end{array}$

    

The triangle is an isosceles triangle.

Thus 

Side opposite to the equal angles are equal. 

Therefore,$\left(l\right)=\left(b\right)=\frac{7}{\sqrt{2}}$

 

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

     Now,  area of the figure

 $\begin{array}{c}A=(l\times b)\\ =\left(\frac{7}{\sqrt{2}}\right)\times \left(\frac{7}{\sqrt{2}}\right)\\ =\frac{49}{2}sq.units\end{array}$

 

Therefore, the area of the figure  $\left(A\right)=\frac{49}{2}sq.units$