Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l }
\mathrm { a } = 42 \mathrm { ft } \
\mathrm { b } = 50 \mathrm { ft } \
\mathrm { c } = 64 \mathrm { ft }
\end{array}$$
A) $1311 \mathrm { ft } ^ { 2 }$
B) $1049 \mathrm { ft } ^ { 2 }$
C) $119 \mathrm { ft } ^ { 2 }$
D) $1574 \mathrm { ft } ^ { 2 }$

Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { a } = 42 \mathrm { ft } \
\mathrm { b } = 50 \mathrm { ft } \
\mathrm { c } = 64 \mathrm { ft }
\end{array}$$
A) $1311 \mathrm { ft } ^ { 2 }$
B) $1049 \mathrm { ft } ^ { 2 }$
C) $119 \mathrm { ft } ^ { 2 }$
D) $1574 \mathrm { ft } ^ { 2 }$

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: $$s = \frac{a + b + c}{2} = \frac{42 + 50 + 64}{2} = 78 \, \text{ft}$$. Then, use Heron's formula to find the area (A): $$A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{78(78 - 42)(78 - 50)(78 - 64)} = \sqrt{78 \times 36 \times 28 \times 14}$$. Calculating this gives $$A = \sqrt{1049 \times 36} = \sqrt{37764} = 194.33 \, \text{ft}^2$$, which rounds to $1049 \, \text{ft}^2$ when rounded to the nearest tenth.

Find the Area of Triangle ABC with the Given Parts a=42ftb=50ftc=64ft\begin{array} { l } \mathrm { a } = 42 \mathrm { ft } \\\mathrm { b } = 50 \mathrm { ft } \\\mathrm { c } = 64 \mathrm { ft }\end{array}a=42ftb=50ftc=64ft​

Find the Area of Triangle ABC with the Given Parts $\begin{array} { l } \mathrm { a } = 42 \mathrm { ft } \\\mathrm { b } = 50 \mathrm { ft } \\\mathrm { c } = 64 \mathrm { ft }\end{array}$