Chapter 11.4, Problem 38HP

To determine

To Find: Whether the enough information is provided to determine the area of the shaded figure and then find the area to the nearest square millimetre if not what additional information is needed explain.

Answer to Problem 38HP

The area of the shaded region is $1146.58$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the area of the region is,

  $A_{shadeed}=A_{ABCD}-A_{\Delta AED}$

Obtain the value of DE by Pythagorean Theorem as,

  $\begin{array}{l}D{E}^2=A{D}^2-A{E}^2\\ D{E}^2={80}^2-{78}^2\\ D{E}^2=316\\ DE=17.78\end{array}$

Then, the area of the triangle AED is,

  $\begin{array}{c}\Delta AED=\frac{AE\cdot DE}{2}\\ =\frac{78\left(17.78\right)}{2}\\ =693.42\end{array}$

The area of ABCD is determined as,

  $\begin{array}{c}AB\cdot BC=23\left(80\right)\\ =1840\end{array}$

Then, the area of the shaded region is,

  $1840-693.42=1146.58$