Question

Area(Multistep)In PQR, p = 14 inches, q = 37 inches and r=38 inches. Find the area of PQR to thenearest 10th of an square inch.

Answer 1

Answer:

257.2 square inches

Explanation:

Given the three sides of a triangle, the area is found using Heron's formula:

$\begin{gathered} \text{Area}=\sqrt[]{s(s-p)(s-q)(s-r)} \\ \text{Where p,q,r are the side lengths} \\ s=\frac{p+q+r}{2} \end{gathered}$

First, find the value of s:

$s=\frac{14+37+38}{2}=\frac{89}{2}=44.5\text{ inches}$

Next, substitute the values into the formula:

$\begin{gathered} \text{Area}=\sqrt[]{s(s-p)(s-q)(s-r)} \\ =\sqrt[]{44.5(44.5-14)(44.5-37)(44.5-38)} \end{gathered}$

Finally, simplify:

$\begin{gathered} =\sqrt[]{44.5(30.5)(7.5)(6.5)} \\ =\sqrt[]{66165.9375} \\ =257.23 \\ \approx257.2\text{ square inches} \end{gathered}$

The area of triangle PQR is 257.2 square inches (to the nearest 10th of a square inch).