Given $a = 5 , b = 9$, and $c = 12$, use Heron's Area Formula to find the area of triangle $A B C$. Round answer to two decimal places.
A) $20.40 \mathrm { sq }$. units
B) $16.97$ sq. units
C) $19.60$ sq. units
D) $12.65$ sq. units
E) $17.40$ sq. units

Question

Quizplus · Accepted Answer

Heron's Area Formula: $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semiperimeter, $s = \frac{a + b + c}{2}$.$s = \frac{5 + 9 + 12}{2} = 13$$A = \sqrt{13(13-5)(13-9)(13-12)} = \sqrt{13(8)(4)(1)} = \sqrt{416} \approx 20.40$ sq. units

Given a=5,b=9a = 5 , b = 9a=5,b=9 , And c=12c = 12c=12

Given $a = 5 , b = 9$ , And $c = 12$