Q24. - Geometry

Question

Find the area of given figure? 

Step-by-Step Solution

Answer

Area of the figure   $\left(A\right)=34y^2$

Step 1. Given information.

Consecutive sides of the figure is perpendicular.

Step 2. Concept Used.

If b is the base of the reactangle and  i is the height of the rectangle.

Then, the   area of the rectangle is 
 $A=b\times l$

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

  Value of first part of the figure is –height   $\left(l\right)=y,$ $base\left(b\right)=2y$

 

 Put the value of base and height  into the formula and find the area of the figure:

 $\begin{array}{c}{A}_1=\left(2y\right)\times \left(y\right)\\ =2y^2\end{array}$

Value of the second part of the figure is-height    $\left(l\right)=2y,$$base\left(b\right)=4y$

Put the value of base and height  into the formula and find the area of the figure: 

 $\begin{array}{c}{A}_2=\left(4y\right)\times \left(2y\right)\\ =8y^2\end{array}$

Value of the third part of the figure is –height    $\left(l\right)=3y,$$base\left(b\right)=8y$

 Put the value of base and height  into the formula and find the area of the figure:$\begin{array}{c}{A}_3=\left(8y\right)\times \left(3y\right)\\ =24y^2\end{array}$

 

 Now,

The total area of the figure –$\begin{array}{l}A=A_1+A_2+A_3\\ A=2y^2+8y^2+24y^2\\ A=34y^2\end{array}$

 

Therefore, the area of the figure  $\left(A\right)=34y^2$