# A line segment inside a square is perpendicular to another line segment that is also inside the square. Find the area in the diagram shown

$$ABCD$$ is a square. $$|AH|=2$$ cm, $$|EH|=6$$ cm.

$$FE||AB$$

Find $$A(ABEF)$$.

There are only few known, so I tried to find some similarities by naming the angles in the right triangles, but I couldn't set up the ratios.

How can I solve this problem?

Let $$|AB|=:s$$, $$\>|BE|=:h$$. Since $$\triangle(AHD)\sim\triangle(EBA)$$ we have $${2\over s}={h\over2+6}$$ and therefore $${\rm area}(ABEF)=hs=16\ .$$