Answer
$A = 15\sqrt{3}$
We also find this area when we use Heron's formula.
Work Step by Step
We can find the area of the triangle:
$A = \frac{1}{2}bh$
$A = \frac{1}{2}(10)(3\sqrt{3})$
$A = 15\sqrt{3}$
We can find the semiperimeter of the triangle:
$S = \frac{a+b+c}{2}$
$S = \frac{6+10+14}{2}$
$S = 15$
We can use Heron's formula to find the area of the triangle:
$A = \sqrt{S(S-a)(S-b)(S-c)}$
$A = \sqrt{15(15-6)(15-10)(15-14)}$
$A = \sqrt{675}$
$A = 15\sqrt{3}$
