What is the area of triangle ABC?

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

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step-by-step explanation:

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