Question

the sides of a triangle measure 7 in, 11 in, and 16 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

The semi - perimeter \(s=\frac{a + b + c}{2}\), where \(a = 7\), \(b = 11\), \(c = 16\).
\(s=\frac{7+11 + 16}{2}=\frac{34}{2}=17\)

Step2: Use Heron's formula

Heron's formula for the area of a triangle is \(A=\sqrt{s(s - a)(s - b)(s - c)}\)
Substitute \(s = 17\), \(a = 7\), \(b = 11\), \(c = 16\) into the formula:
\(A=\sqrt{17(17 - 7)(17 - 11)(17 - 16)}=\sqrt{17\times10\times6\times1}=\sqrt{1020}\approx31.9\)

Answer:

\(31.9\)