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△BCD is a special right triangle called a " 30-60-90 triangle "  because its angles are 30°, 60°, and 90°.

 

In every 30-60-90 triangle, if the side opposite the 30° angle is  n , then

the side opposite the 60° angle is  n√3  and the side opposite the 90° angle is 2n

 

 

In △BCD, the side opposite the 30° is  12 , so

the side opposite the 60° angle is  12√3  and the side opposite the 90° angle is  2(12) .

 

So.....

 

BC = 12√3

BD =  2(12)  =  24

 

height of the triangle  =  12√3  cm

 

area of triangle  =  ( 1/2 )( base )( height )

area of triangle  =  ( 1/2 )( 12 )( 12√3 )  cm2               I'll let you simplify this.

 May 31, 2019

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