Chapter 6.2, Problem 57E

To determine

The area of the parcel.

Answer to Problem 57E

The area of the parcel is 46837.5feet².

Explanation of Solution

Given:

The triangular parcel has the land sides of the 200feet, 500feet and 600 feet.

Considering the three sides of the parcels as:

  $\begin{array}{l}a=200\\ b=500\\ c=600\end{array}$

Now, evaluating the value of the s:

  $\begin{array}{l}s=\frac{a+b+c}{2}\\ =\frac{200+500+600}{2}\\ =650\end{array}$

Now, evaluating the area of the triangle using the Heron’s formula:

  $\begin{array}{l}\text{Area=}\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ =\sqrt{650\left(650-200\right)\left(650-500\right)\left(650-600\right)}\\ =46837.5{\text{feet}}^2\end{array}$

Therefore, the area of the parcel is 46837.5feet².