Question

What is the area of triangle ABC?

Answer 1

Answer:

C

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

The triangle is equilateral , since 3 angles = 60°

Then base AB = 12

Find height CD using the sine ratio in the right triangle ( there are 2 )

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{CD}{BC}$ = $\frac{CD}{12}$ = $\frac{\sqrt{3} }{2}$ ← exact value of sin60° ( cross- multiply )

2CD = 12$\sqrt{3}$ ( divide both sides by 2 )

CD = 6$\sqrt{3}$

Then

A = $\frac{1}{2}$ × 12 × 6$\sqrt{3}$ = 6 × 6$\sqrt{3}$ = 36$\sqrt{3}$ units² → C