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# geometry

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In the figure below, side $AE$ of rectangle $ABDE$ is parallel to the $x$-axis, and side $BD$ contains the point $C$. The vertices of triangle $ACE$ are $A(1, 1)$, $C(3, 5)$ and $E(4, 1)$. What is the ratio of the area of triangle $ACE$ to the area of rectangle $ABDE$?

Jan 10, 2022

Note that $$\triangle ACE$$ and $$ABDE$$ have the same base and height, and since the area of a rectangle is equal to $$bh$$ and the area of a triangle is equal to $$\frac{bh}{2}$$, we get that $$\frac{[\triangle ACE]}{[ABDE]} = \boxed{\frac{1}{2}}$$.