Question

The dimensions of home plate at any major league baseball stadium are shown. Find the area of home plate.

Short answer

The area of the baseball home plate is$216.5i{n}^2$

Step-by-step solution

Given information

We are given

We divide the image in two parts A triangle and a rectangle

We get,

Find the area of triangle

First we calculate

$$\begin{gathered} s=\frac{1}{2}(12+12+17) \\ s=20.5 \end{gathered}$$

Now area of triangle can be given as

$$\begin{gathered} K=\sqrt{s(s-a)(s-b)(s-c)} \\ K=\sqrt{20.5(20.5-12)(20.5-12)(20.5-17)} \\ K=\sqrt{20.5(8.5)(8.5)(3.5)} \\ K=\sqrt{5183.9375} \\ K=72i{n}^2 \end{gathered}$$

Area of rectangle

We have

$$\begin{gathered} A=l\times b \\ A=8.5\times 17 \\ A=144.5i{n}^2 \end{gathered}$$

Find the area of the baseball plate

The area can be given as

$$\begin{gathered} K_b=K+A \\ {K}_b=72+144.5 \\ {K}_b=216.5i{n}^2 \end{gathered}$$

Conclusion

Area of the baseball plate is$216.5i{n}^2$