Chapter 8.4, Problem 37AYU

To determine

To find: The area of the Home plate.

Answer to Problem 37AYU

The area of the plate is $216.5{\text{in}}^2$ .

Explanation of Solution

Given:

The given diagram for the Home plate is shown in Figure

  

Figure 1

Calculation:

Consider the area of the home plate is the area of the upper triangle plus the area of the rectangle that is,

  $A=\sqrt{s\left(s-12\right)\left(s-12\right)\left(s-17\right)}+\left(8.5\right)\left(1.7\right)$

Consider the semi perimeter of the triangle is,

  $\begin{array}{c}s=\frac{12+12+17}{2}\\ =20.5\end{array}$

Then,

  $\begin{array}{c}A=\sqrt{20.5\left(20.5-12\right)\left(20.5-12\right)\left(20.5-17\right)}+\left(8.5\right)\left(1.7\right)\\ =\sqrt{5183.9375}+144.5\\ \approx 72+144.5\\ =216.5{\text{in}}^2\end{array}$