Chapter 11.9, Problem 25HP

To determine

Todescribe:and estimate the area of the composite figures

Answer to Problem 25HP

  $91.71{\text{cm}}^2$ .

Explanation of Solution

Given:

A composite figure has a curved that is not the semicircle.

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.

Here composite figure has a curved that is not the semicircle.

For example: consider a square and an equilateraltriangle is drawn on the top of the square.

  

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

Now, divide the given figure in tothe squaredimensions is 8cmand t triangle

Area A of the triangle is given by the formula $A=\frac{\sqrt{3}}{4}{a}^2$ where a is the side.

The area A of the square is given by the formula $A={\text{side}}^2$ .

Thus, area A of the square is given by

  $\begin{array}{l}A={\text{side}}^2\\ ={\left(8cm\right)}^2=64c{m}^2\end{array}$

And the area A of the equilateral triangle is given

  $\begin{array}{l}A=\frac{\sqrt{3}}{4}{a}^2\\ =\frac{\sqrt{3}}{4}{\left(8\right)}^2\\ =16\sqrt{3}c{m}^2=27.71c{m}^2\end{array}$

Thus, the required area of the figure is the sum of the area of the equilateral triangle, plus the area of the square

Therefore, $A=64+27.71=91.71{\text{cm}}^2$

Hence, the required area of figure is $91.71{\text{cm}}^2$ .