Given $a = 13 , b = 11$, and $c = 6$, use Heron's Area Formula to find the area of triangle $A B C$. Round answer to two decimal places.
A) $32.86$ sq. units
B) $28.14$ sq. units
C) $20.78$ sq. units
D) $30.59$ sq. units
E) $28.10$ sq. units

Question

Quizplus · Accepted Answer

Heron's formula for the area of a triangle with sides of lengths $a$, $b$, and $c$ is given by $\sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a+b+c}{2}$ is the semi-perimeter of the triangle. For $a = 13$, $b = 11$, and $c = 6$, the semi-perimeter $s = \frac{13+11+6}{2} = 15$. Plugging these values into Heron's formula gives the area as $\sqrt{15(15-13)(15-11)(15-6)} = \sqrt{15 \times 2 \times 4 \times 9} = \sqrt{1080} = 32.86$ square units, rounded to two decimal places.

Given a=13,b=11a = 13 , b = 11a=13,b=11 , And c=6c = 6c=6

Given $a = 13 , b = 11$ , And $c = 6$