Answer:
D. 72.6 mm²
Explanation:
The area of the triangle can be calculated by Heron's Formula:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]Where a, b, and c, are the legs and s can be calculated as:
[tex]s=\frac{a+b+c}{2}[/tex]Therefore, replacing a, b, and c by 15, 10, and 20, we get that s is equal to:
[tex]\begin{gathered} s=\frac{15+10+20}{2} \\ s=\frac{45}{2} \\ s=22.5 \end{gathered}[/tex]Then, the area of the triangle will be equal to:
[tex]\begin{gathered} A=\sqrt[]{22.5(22.5-15)(22.5-10)(22.5-20)} \\ A=\sqrt[]{22.5(7.5)(12.5)(2.5)} \\ A=\sqrt[]{5273.44} \\ A=72.6mm^2 \end{gathered}[/tex]So, the answer is:
D. 72.6 mm²
