Thank you for visiting Find the area of a triangle with legs that are 16 m 12 m and 8 m A 38 2 m² B 46 5 m². This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To calculate the area of a triangle with 3 sides given, we use Heron's formula.
Heron's formula is given below;
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where s is the semi perimeter} \\ s=\frac{a+b+c}{2} \\ \text{where } \\ a=8m \\ b=12m \\ c=16m \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} s=\frac{8+12+16}{2} \\ s=\frac{36}{2} \\ s=18m \end{gathered}[/tex][tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{18(18-8)(18-12)(18-16)} \\ A=\sqrt[]{18\times10\times6\times2} \\ A=\sqrt[]{2160} \\ A=\pm46.4758m^2 \\ \text{Area cannot be negative, thus} \\ A=46.4758m^2 \\ A\approx46.5m^2 \end{gathered}[/tex]Therefore, the area of the triangle with legs 16m, 12m, and 8m is 46.5 square meters
The correct answer is option B.
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Rewritten by : Jeany
