Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l }
a = 18.6 \mathrm {~cm} \
b = 17.2 \mathrm {~cm} \
c = 15.0 \mathrm {~cm}
\end{array}$$
A) $124 \mathrm {~cm} ^ { 2 }$
B) $121 \mathrm {~cm} ^ { 2 }$
C) $130 \mathrm {~cm} ^ { 2 }$
D) $127 \mathrm {~cm} ^ { 2 }$

Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
a = 18.6 \mathrm {~cm} \
b = 17.2 \mathrm {~cm} \
c = 15.0 \mathrm {~cm}
\end{array}$$
A) $124 \mathrm {~cm} ^ { 2 }$
B) $121 \mathrm {~cm} ^ { 2 }$
C) $130 \mathrm {~cm} ^ { 2 }$
D) $127 \mathrm {~cm} ^ { 2 }$

Quizplus · Accepted Answer

To find the area of a triangle given the lengths of all three sides, you can use Heron's formula. First, calculate the semi-perimeter (s) of the triangle: $s = \frac{a + b + c}{2}$. Then, use Heron's formula: $\sqrt{s(s - a)(s - b)(s - c)}$. Plugging in the given values: $s = \frac{18.6 + 17.2 + 15.0}{2} = 25.4$. The area is then $\sqrt{25.4(25.4 - 18.6)(25.4 - 17.2)(25.4 - 15.0)} \approx 121 \mathrm{cm}^2$.

Find the Area of Triangle ABC with the Given Parts a=18.6 cmb=17.2 cmc=15.0 cm\begin{array} { l } a = 18.6 \mathrm {~cm} \\b = 17.2 \mathrm {~cm} \\c = 15.0 \mathrm {~cm}\end{array}a=18.6 cmb=17.2 cmc=15.0 cm​

Find the Area of Triangle ABC with the Given Parts $\begin{array} { l } a = 18.6 \mathrm {~cm} \\b = 17.2 \mathrm {~cm} \\c = 15.0 \mathrm {~cm}\end{array}$