Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-Find the area of a triangular garden if the sides are approximately 6 feet, 11 feet, and 12 feet (to the nearest square foot).
A) $33 \mathrm { ft } ^ { 2 }$
B) $9 \mathrm { ft } ^ { 2 }$
C) $396 \mathrm { ft } ^ { 2 }$
D) $448 \mathrm { ft } ^ { 2 }$

Question

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: $s = \frac{a + b + c}{2}$, where $a$, $b$, and $c$ are the lengths of the sides. For this triangle, $s = \frac{6 + 11 + 12}{2} = 14.5$ feet. Then, use Heron's formula to find the area ($A$): $A = \sqrt{s(s - a)(s - b)(s - c)}$. Plugging in the values, $A = \sqrt{14.5(14.5 - 6)(14.5 - 11)(14.5 - 12)} \approx 33 \mathrm { ft } ^ { 2 }$.

Find the Area of Triangle ABC with the Given Parts 33ft233 \mathrm { ft } ^ { 2 }33ft2

Find the Area of Triangle ABC with the Given Parts $33 \mathrm { ft } ^ { 2 }$