Solve the problem.
-Tia is going to stain her triangular concrete patio. The patio is approximately 10 feet by 17 feet by 13 feet. If one can of stain covers $17 \mathrm { ft } ^ { 2 }$, how many cans of stain will she need?
A) 65 cans
B) 51 cans
C) 4 cans
D) 1 cans

Question

Quizplus · Accepted Answer

To find the area of the triangular patio, we can use Heron's formula since we have the lengths of all three sides. First, calculate the semi-perimeter (s) as $s = \frac{a + b + c}{2}$, where $a$, $b$, and $c$ are the lengths of the sides. So, $s = \frac{10 + 17 + 13}{2} = 20$. Then, the area ($A$) of the triangle can be calculated using $A = \sqrt{s(s - a)(s - b)(s - c)}$, which gives $A = \sqrt{20(20 - 10)(20 - 17)(20 - 13)} = \sqrt{20 \times 10 \times 3 \times 7} = \sqrt{4200}$ square feet. The square root of 4200 is approximately 64.81 square feet. Since one can of stain covers 17 square feet, Tia will need $\frac{64.81}{17} \approx 3.81$ cans. Since she can't buy a fraction of a can, she will need to round up to the nearest whole number, which means she will need 4 cans of stain.

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