Find the area of the triangle shown !

Geometry Level pending

Find the area of the triangle shown above.


The answer is 66.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The area of the triangle is equal to the area of the rectangle circumscribing the triangle minus the sum of the areas of the three small triangles. We have

A = 12 ( 12 ) − 1 2 [ 2 ( 12 ) + 10 ( 6 ) + 6 ( 12 ) ] = 144 − 1 2 ( 156 ) = 66 A=12(12)-\dfrac{1}{2}[2(12)+10(6)+6(12)]=144-\dfrac{1}{2}(156)=\boxed{66}

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