Question

the sides of a triangle measure 16 yd, 37 yd, and 25 yd. find its area. write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Calculate the semi - perimeter

Let \(a = 16\), \(b = 37\), \(c = 25\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{16+37 + 25}{2}=\frac{78}{2}=39\).

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 \(s = 39\), \(a = 16\), \(b = 37\), \(c = 25\) into the formula: \(A=\sqrt{39(39 - 16)(39 - 37)(39 - 25)}=\sqrt{39\times23\times2\times14}=\sqrt{39\times23\times28}=\sqrt{39\times644}=\sqrt{25116}=158.5\).

Answer:

\(158.5\)