Question

What is the Area and perimeter of triangle HAB?

Answer 1

bearing in mind that there are 90 feet between each base in a baseball diamond, so the total perimeter of it will be 90*4 = 360, one third of that is 360/3 = 120.

So Jones went 120 feet first and then another and so on, check the picture below.

using those values, can get the length of those sides, using the pythagorean theorem.

$\bf AH=\sqrt{HF^2+FA^2}\implies AH=\sqrt{9000} \\\\\\ AB=\sqrt{AS^2+SB^2}\implies AB=\sqrt{7200} \\\\\\ HB = AH = \sqrt{9000} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{perimeter}{\sqrt{9000}+\sqrt{7200}+\sqrt{7200}}\qquad \approx \qquad \stackrel{perimeter}{264.57}$

now, we can plug those values in the Heron's Area Formula to get its area.

$\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{9000}\\ b=\sqrt{7200}\\ c=\sqrt{7200}\\ s\approx 132.29 \end{cases} \\\\\\ A=\sqrt{132.29(132.29-\sqrt{9000})(132.29-\sqrt{7200})(132.29-\sqrt{7200})} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 3337.289~\hfill$