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

257.2 square inches

Step-by-step 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=(p+q+r)/(2) \end{gathered}`

First, find the value of s:

`s=(14+37+38)/(2)=(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).