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2021 Fall AMC 12B Problem 2

Problem 2 of 25EasierGeometry

What is the area of the shaded figure shown below?

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Solution

The outer triangle has vertices (1,0),(1, 0), (3,5),(3, 5), and (5,0),(5, 0), giving base 44 and height 5,5, so its area is 12⋅4⋅5=10.\tfrac12 \cdot 4 \cdot 5 = 10. Removed from it is the triangle with vertices (1,0),(1, 0), (3,2),(3, 2), and (5,0),(5, 0), which has base 44 and height 2,2, so area 12⋅4⋅2=4.\tfrac12 \cdot 4 \cdot 2 = 4. The shaded area is 10−4=6.10 - 4 = 6. Thus, the correct answer is B.
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Tagged: triangle area · area decomposition

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