Question

What is the area of triangle ABC?

Answer 1

C.

Explanation:

It is an equilateral triangle.

DB = 6, AB = 12, DC = height

`DC=\sqrt{(CB)^(2)- (DB)^(2) } =√(144-36) =√(108)=√((36)(3)) =6√(3)`

`A=((DC)(AC))/(2) =((6√(3))(12) )/(2) =(72√(3) )/(2) =36√(3)`

Hope this helps

Answer 2

two angles in the triangle are 60°, so the last one must be 60°, since all must add up to 180°, that means the triangle is equilateral

`\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2√(3)}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2√(3)}{4}\implies A=36√(3)~ ~~ units^2`