Question

the sides of a triangle measure 42 cm, 41 cm, and 35 cm. find its area. write your answer as an integer or as a decimal rounded to the nearest tenth. cm²

Explanation:

Step1: Calculate the semi - perimeter

The semi - perimeter \(s=\frac{a + b + c}{2}\), where \(a = 42\), \(b = 41\), \(c = 35\).
\(s=\frac{42+41 + 35}{2}=\frac{118}{2}=59\)

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 \(s = 59\), \(a = 42\), \(b = 41\), \(c = 35\) into the formula:
\(A=\sqrt{59(59 - 42)(59 - 41)(59 - 35)}\)
\(=\sqrt{59\times17\times18\times24}\)
\(=\sqrt{59\times17\times432}\)
\(=\sqrt{59\times7344}\)
\(=\sqrt{433296}\)
\(=658\)

Answer:

\(658\)