Chapter 11.1, Problem 22WE

To determine

To Find: The area of the figure.

Answer to Problem 22WE

  $A=\frac{49}{2}sq.units$

Explanation of Solution

Given: Consecutive sides of the figure is perpendicular.

  

  

  $\begin{array}{l}\Delta BCDis\\ {45}^{°}-{45}^{°}-{90}^{°}\end{array}$

Thus

  $\begin{array}{l}H=\sqrt{2}\cdot B\\ B=\frac{H}{\sqrt{2}}\\ B=\frac{7}{\sqrt{2}}\end{array}$

The triangle is an isosceles triangle

Thus

Side opposite to the equal angles are equal.

Therefore,

  $P(l)=B(b)=\frac{7}{\sqrt{2}}$

Now

Area of figure

  $\begin{array}{l}A=lb\\ A=\frac{7}{\sqrt{2}}\cdot \frac{7}{\sqrt{2}}\\ A=\frac{49}{2}sq.units\end{array}$

Hence, $A=\frac{49}{2}sq.units$