The above shows a triangle with area 15, and given side length .
A square is inscribed inside this triangle such that and lies on the line .
What is the sum of areas of the triangles and ?
Give your answer to 2 decimal places.
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A T = 2 1 b h
1 5 = 2 1 ( 1 0 ) h
h = 3
x = b + h b h = 1 3 3 0
A s h a d e d = A T − A A D G − A s q u a r e = 1 5 − [ 2 1 ( 1 3 3 0 ) ( 3 − 1 3 3 0 ) ] + ( 1 3 3 0 ) 2 = 8 . 8 8 s q u a r e u n i t s