Chapter 11, Problem 33SGR

To determine

To find: The area of the figure.

Answer to Problem 33SGR

The area of each figure is $18,4.5$ .

Explanation of Solution

Given information: Figure of triangle is given.

Calculation: Figure of triangle is given.

Base of triangle $=6$ .

Height of triangle $=6$ .

Area of triangle:

  $\begin{array}{l}=\frac{1}{2}\times b\times h\\ =\frac{1}{2}\times 6\times 6\\ =3\times 6\\ =18\end{array}$

  $\begin{array}{l}\mathrm{Area}ofsimilartriangle=ratiothesquareofcorrespondingsides\\ \mathrm{Area}ofsimilartriangle={\left(\frac{RS}{R\text{'}S\text{'}}\right)}^2\\ \frac{18}{x}={\left(\frac{6}{3}\right)}^2\\ \frac{18}{x}={\left(2\right)}^2\\ \frac{18}{x}=4\\ 18=4x\\ \frac{18}{4}=x\\ 4.5=x\end{array}$

Thus the area of each figure is $18,4.5$ .