Chapter 11.2, Problem 15PSB

To determine

To find the area of the shaded region.

Answer to Problem 15PSB

The area of the shaded region is $85$ units.

Explanation of Solution

Given:

  $\begin{array}{l}AB=DC=10,\\ AD=BC=17\end{array}$

Formula Used:

  $\begin{array}{l}Areaofrectangle=b\ast h\\ b=Base,\\ h=Height\end{array}$

  $\begin{array}{l}Areaoftriangle=\frac{1}{2}\ast b\ast h\\ b=Base,\\ h=Height\end{array}$

Calculation:

  $\begin{array}{l}Areaofrectangle=b\ast h\\ A(\square ABCD)=BC*AB=17*10=170\end{array}$

  $\begin{array}{l}Areaoftriangle=\frac{1}{2}\ast b\ast h\\ A(\Delta BEC)=\frac{1}{2}\ast BC\ast ED\\ \end{array}$

  $ED=DC=10$

  $\begin{array}{l}A(\Delta BEC)=\frac{1}{2}*BC*DC\\ =\frac{1}{2}*17*10\\ =85\end{array}$

  $\begin{array}{l}Areaofshadedregion=Areaofrectangle-Areaoftriangle\\ =A(\square ABCD)-A(\Delta BEC)\\ =170-85\\ =85units\end{array}$