Question

the sides of a triangle measure 8 mm, 12 mm, and 18 mm. find its area. write your answer as an integer or as a decimal rounded to the nearest tenth.

\boxed{} mm²

Explanation:

Step1: Use Heron's formula. First, find the semi-perimeter \( s \).

The formula for semi - perimeter \( s=\frac{a + b + c}{2}\), where \( a = 8\), \( b = 12\), \( c = 18\).
\(s=\frac{8 + 12+18}{2}=\frac{38}{2}=19\)

Step2: Apply Heron's formula for area \( A=\sqrt{s(s - a)(s - b)(s - c)}\)

Substitute \( s = 19\), \( a = 8\), \( b = 12\), \( c = 18\) into the formula:
\(A=\sqrt{19(19 - 8)(19 - 12)(19 - 18)}\)
\(=\sqrt{19\times11\times7\times1}\)
\(=\sqrt{19\times77}\)
\(=\sqrt{1463}\approx38.3\)

Answer:

\(38.3\)