Answer
$216.5 \ in^2$
Work Step by Step
The top part of the triangle has sides $12, 12$ and $17$. By Heron's formula, the area of a triangle with sides $a,b$ and $c$ is given by:
$K=\sqrt{s(s-a)(s-b)(s-c)}$;
where $s=\dfrac{a+b+c}{2}$
Therefore, $s=\dfrac{12+12+17}{2}=20.5$
and $K=\sqrt{20.5(20.5-12)(20.5-12)(20.5-17)}\approx 72$
The bottom part the triangle has length $17 \ inches$ and the width is $8.5 \ inches$. So, the area becomes: $(17)(8.5) =144.5$
Now, the total area of the home plate is equal to
$72+144.5 =216.5 \ in^2$
