Chapter 11.9, Problem 26HP

To determine

Tofind:the area of the composite figures by using circles and polygons. Given an example by drawing and labelling a composite figure. Describe the figure to find the area and then find area.

Answer to Problem 26HP

  $294{\text{cm}}^2$ .

Explanation of Solution

Given:

A composite figure is formed by circles and polygons.

Calculation:

A composite figure is made up of several simple geometric figures such as triangles, rectangles, squares, circles, and semicircles. To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together. Be sure than none of the simpler figures have overlapping areas.

For example: consider a rectangle whose length is 20 cm and its width is 7 cm and a semicircle is drawn on both sides of the width.

  

The objective is to find the area of the composite figure.

Now, divide the given figure in to twosemicircles of equal dimensions, which is circle and a rectangle of dimensions 20 cm and 7 cm, which is polygon.

The area A of a two semicircle is given by the formula $A=2\times \frac{1}{2}\pi r^2=\pi r^2$ where r is the radius.

The area A of the rectangle is given by the formula $A=lw$ where l is the length andw is the width.

Thus, area A of the circle is given by

  $\begin{array}{l}A=\pi r^2\\ =\frac{22}{7}{\left(7\right)}^2\{\because \pi =\frac{22}{7}\}\\ =154c{m}^2\end{array}$

And the area A of the rectangle is given

  $\begin{array}{l}A=lw\\ =\left(20\right)\left(7\right)=140c{m}^2\end{array}$

Thus, the required area of the figure is the sum of the area of 2 semicircle, and one rectangle

Therefore, $A=154+140=294{\text{cm}}^2$

Hence, the required area of figure is $294{\text{cm}}^2$ .