Question

What is the area of triangle ABC?

Select the correct choice.

A: 6sqrt3
B: 18sqrt3
C: 36sqrt3
D: 72sqrt3

Answer 1

C

Explanation:

The area (A) of the triangle is calculated as

A =
`(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° =
`(opposite)/(hypotenuse)` =
`(CD)/(BC)` =
`(CD)/(12)` =
`(√(3) )/(2)` ← exact value of sin60° ( cross- multiply )

2CD = 12
`√(3)` ( divide both sides by 2 )

CD = 6
`√(3)`

Then

A =
`(1)/(2)` × 12 × 6
`√(3)` = 6 × 6
`√(3)` = 36
`√(3)` units² → C