Question

What is the area of triangle ABC?​

Answer 1

To find the area of triangle ABC, we need the base and height measurements. Unfortunately, the information given in the question is not sufficient to calculate the area. We need either the base or the height measurement.

Step-by-step explanation:

The formula for the area of a triangle is 1/2 × base x height. To find the area of triangle ABC, we need the base and height measurements. Unfortunately, the information given in the question is not sufficient to calculate the area. We need either the base or the height measurement.

Answer 2

C

Step-by-step explanation:

Remark

The large triangle with 2 60 degree angles is equilateral. Therefore the line at D can be shown to be at right angles to AB and D is the midpoint of AB.

Solution

1/2 of AB is 6 See the discussion above.

DB is the base of CBD in the right triangle CDB

h^2 + DB^2 = 12^2

h^2 + 6^2 = 12^2

h^2 = 144 - 36

h^2 = 108

h = sqrt(108)

h = sqrt(9*3 * 4

sqrt(9) = 3

sqrt(4) = 2

So the square root of 108 = 3*2 sqrt(3) because there is 1 three that is left over.

h = 6*sqrt(3)

base = 12

Area = 1/2 * 6*sqrt3) * 12

Area = 36 sqrt(3)

The answer is C