2020 AMC 12B Problems/Problem 18
In square , points and lie on and , respectively, so that Points and lie on and , respectively, and points and lie on so that and . See the figure below. Triangle , quadrilateral , quadrilateral , and pentagon each has area What is ?
Solution
Plot a point such that and are collinear and extend line to point such that forms a square. Extend line to meet line F'B' and point is the intersection of the two. The area of this square is equivalent to . We see that the area of square is , meaning each side is of length 2. The area of the quadrilateral is . Length , thus . Triangle is isosceles, and the area of this triangle is . Adding these two areas, we get .
2020 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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