Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-Tia is going to stain her triangular concrete patio. The patio is approximately 14 feet by 18 feet by 10 feet. If one can of stain covers $12 \mathrm { ft } ^ { 2 }$, how many cans of stain will she need?
A) 6 cans
B) 79 cans
C) 2 cans
D) 105 cans

Question

Quizplus · Accepted Answer

To find the area of a triangle given three sides, we can use Heron's formula. First, calculate the semi-perimeter (s) as $s = \frac{a + b + c}{2}$, where $a$, $b$, and $c$ are the lengths of the sides. Here, $s = \frac{14 + 18 + 10}{2} = 21$. Then, the area ($A$) can be found using $A = \sqrt{s(s - a)(s - b)(s - c)}$, which gives $A = \sqrt{21(21 - 14)(21 - 18)(21 - 10)} = \sqrt{21 \times 7 \times 3 \times 11} = \sqrt{4851}$ square feet. The exact area is approximately 69.6 square feet. Since one can covers $12 \mathrm { ft } ^ { 2 }$, she needs $\frac{69.6}{12} \approx 5.8$ cans. Rounding up, Tia needs 6 cans of stain.

Find the Area of Triangle ABC with the Given Parts 12ft212 \mathrm { ft } ^ { 2 }12ft2

Find the Area of Triangle ABC with the Given Parts $12 \mathrm { ft } ^ { 2 }$