Question

In ∆PQR, p=13 inches, q=18 inches and r= 12 inches. Find the area of ∆PQR to the nearest square inch.

Answer 1

Given data:

The first side of the triangle is p=13 inches.

The second side of the triangle is q=18 inches.

The third side of the triangle is r= 12 inches.

The semi-perimeter is,

$\begin{gathered} s=\frac{p+q+r}{2} \\ =\frac{13\text{ in+18 in+12 in}}{2} \\ =21.5\text{ in} \end{gathered}$

The expression for the area of the triangle is,

$\begin{gathered} A=\sqrt[]{s(s-p)(s-q)(s-r)_{}} \\ =\sqrt[]{21.5\text{ in(21.5 in-13 in)(21.5 in-18 in)(21.5 in-12 in)}} \\ =\sqrt[]{(21.5\text{ in)(8.5 in)(3.5 in)(9.5 in)}} \\ =77.95in^2 \end{gathered}$

Thus, the area of the given triangle is 77.95 sq-inches.