Choose the one alternative that best completes the statement or answers the question.
Find the area of the triangle. If necessary, round the answer to two decimal places.
-a = 4, b = 5, c = 7
A) 10.01
B) 3.46
C) 9.80
D) 16.01

Question

Quizplus · Accepted Answer

The area of a triangle can be found using Heron's formula when the lengths of all three sides are known. Heron's formula is given by $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter of the triangle, calculated as $s = \frac{a + b + c}{2}$. For this triangle, $a = 4$, $b = 5$, and $c = 7$, so $s = \frac{4 + 5 + 7}{2} = 8$. Plugging these values into Heron's formula gives $A = \sqrt{8(8-4)(8-5)(8-7)} = \sqrt{8 \cdot 4 \cdot 3 \cdot 1} = \sqrt{96} \approx 9.80$.

Choose the One Alternative That Best Completes the Statement or Answers