Chapter 12.1, Problem 35SR

To determine

The area of the each figure:

  

Answer to Problem 35SR

The area of the figure is $56.05c{m}^2$ .

Explanation of Solution

Given:

  

Concept Used:

The area of the right angle triangle is given by the following expression:

  $A=\frac{1}{2}\left(a\times b\right)$

Where,

Sides of right angle triangle: $a,b$

The area of the rectangle is given by the following expression:

  $A=l\times w$

Where,

Length of rectangle: $l$

Width of rectangle: $w$

Calculation:

The area of the rectangle is given by the following expression:

  $A_1=l\times w$

Put the given values:

  $\begin{array}{l}{A}_1=l\times w\\ A_1=9.5\times 4\\ A_1=38c{m}^2\end{array}$

The area of the right angle triangle is given by the following expression:

  $\begin{array}{l}{A}_2=\frac{1}{2}\left(a\times b\right)\\ A_2=\frac{1}{2}\left(3.8\times 9.5\right)\\ A_2=18.05c{m}^2\end{array}$

So, the total area of the figure:

  $\begin{array}{l}A=A_1+A_2\\ A=38c{m}^2+18.05c{m}^2\\ A=56.05c{m}^2\end{array}$

Conclusion:

Hence, the area of the figure is $56.05c{m}^2$