Chapter 11.1, Problem 19WE

To determine

To Find: The area of the figure.

Answer to Problem 19WE

  $A=48sq.units$

Explanation of Solution

Given: Consecutive sides of the figure is perpendicular.

  

Since the two triangles are right angles triangle.

Using the Pythagoras theorem

  $\begin{array}{l}B=8\\ H=10\\ P=?\\ H^2=P^2+B^2\\ {10}^2=8^2+P^2\\ 100-64=P^2\\ P^2=36\\ P=6units\end{array}$

Now

Area of triangle

  $\begin{array}{l}A=\frac{1}{2}bh\\ A=\frac{1}{2}(8)(6)\\ A=24sq.units\end{array}$

We know that the diagonal of a rectangle divide it into two equal triangles

Thus

  $\begin{array}{l}A=(2)24\\ A=48sq.units\end{array}$

Hence, $A=48sq.units$