I need help on how to contruct the definite integral needed to find the area of the geometric shape of triangle.

I know that the formula for area of any triangle is A=b*h, where b is the base and h is the perpendicular height from the base to the opposite corner. In the attached picture, I can find the area using slices where the slice thickness is dy and the slice length (y/h)*b. 

Now, how do I be able to contruct the integral and solve to get the formula for the area of this triangle?





Image Transcription

b h y

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