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=√(HF^2+FA^2)\implies AH=√(9000) \\\\\\ AB=√(AS^2+SB^2)\implies AB=√(7200) \\\\\\ HB = AH = √(9000) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{perimeter}{√(9000)+√(7200)+√(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=√(s(s-a)(s-b)(s-c))\qquad \begin{cases} s=(a+b+c)/(2)\\[-0.5em] \hrulefill\\ a=√(9000)\\ b=√(7200)\\ c=√(7200)\\ s\approx 132.29 \end{cases} \\\\\\ A=\sqrt{132.29(132.29-√(9000))(132.29-√(7200))(132.29-√(7200))} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 3337.289~\hfill`