Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.3 Junior Find the answer

The rectangle shown has length $AC=32$ , width $AE=20$ , and $B$ and $F$ are midpoints of $\overline{AC}$ and $\overline{AE}$ , respectively. The area of quadrilateral $ABDF$ is

Pick one

Solution

The area of the quadrilateral $ABDF$ is equal to the areas of the two right triangles $\triangle BCD$ and $\triangle EFD$ subtracted from the area of the rectangle $ABCD$ . Because $B$ and $F$ are midpoints, we know the dimensions of the two right triangles.

$(20)(32)-\frac{(16)(20)}{2}-\frac{(10)(32)}{2} = 640-160-160 = \boxed{\text{(A)}\ 320}$

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