Question

the sides of a triangle measure 31 in, 22 in, and 44 in. find its area. write your answer as an integer or as a decimal rounded to the nearest tenth. in²

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The formula for the semi - perimeter of a triangle with sides \(a\), \(b\), and \(c\) is \(s=\frac{a + b + c}{2}\).
Given \(a = 31\), \(b = 22\), \(c = 44\), then \(s=\frac{31+22 + 44}{2}=\frac{97}{2}=48.5\).

Step2: Use Heron's formula to find the area \(A\)

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\).
Substitute the values: \(A=\sqrt{48.5(48.5 - 31)(48.5 - 22)(48.5 - 44)}\)
\(=\sqrt{48.5\times17.5\times26.5\times4.5}\)
First, calculate \(48.5\times17.5 = 848.75\), \(26.5\times4.5=119.25\)
Then \(848.75\times119.25=101212.3125\)
\(A=\sqrt{101212.3125}\approx318.1\)

Answer:

\(318.1\)