Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l }
a = 47 \mathrm { ft } \
\mathrm { b } = 59 \mathrm { ft } \
\mathrm { c } = 65 \mathrm { ft }
\end{array}$$
A) $1337 \mathrm { ft } ^ { 2 }$
B) $1671 \mathrm { ft } ^ { 2 }$
C) $145 \mathrm { ft } ^ { 2 }$
D) $2006 \mathrm { ft } ^ { 2 }$

Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
a = 47 \mathrm { ft } \
\mathrm { b } = 59 \mathrm { ft } \
\mathrm { c } = 65 \mathrm { ft }
\end{array}$$
A) $1337 \mathrm { ft } ^ { 2 }$
B) $1671 \mathrm { ft } ^ { 2 }$
C) $145 \mathrm { ft } ^ { 2 }$
D) $2006 \mathrm { ft } ^ { 2 }$

Quizplus · Accepted Answer

Using Heron's formula, first calculate the semi-perimeter $s = \frac{a + b + c}{2} = \frac{47 + 59 + 65}{2} = 85.5$ ft. Then, the area $A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{85.5(85.5 - 47)(85.5 - 59)(85.5 - 65)} \approx 1337 \mathrm { ft } ^ { 2 }$.

Find the Area of Triangle ABC with the Given Parts a=47ftb=59ftc=65ft\begin{array} { l } a = 47 \mathrm { ft } \\\mathrm { b } = 59 \mathrm { ft } \\\mathrm { c } = 65 \mathrm { ft }\end{array}a=47ftb=59ftc=65ft​

Find the Area of Triangle ABC with the Given Parts $\begin{array} { l } a = 47 \mathrm { ft } \\\mathrm { b } = 59 \mathrm { ft } \\\mathrm { c } = 65 \mathrm { ft }\end{array}$