Section A Section A Checkpoint
Problem 1
Find the area of each shaded region. Explain or show your reasoning.
Show Solution
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The areas is 16 square units. Sample reasoning:
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The rectangle can be decomposed into 1 square of 4 square units and 6 identical right triangles. Two right triangles make a square of 4 square units, so 6 right triangles make 3 squares with a combined area of 12 square units.
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The rectangle can be enclosed by a 6-by-6 square (36 square units). The square creates 2 larger right triangles and 2 smaller ones. The larger triangles can be rearranged to make a 4-by-4 square (16 square units). The smaller triangles make a 2-by-2 square (4 square units). Subtracting the areas of the triangles from the 6-by-6 square gives 16 square units.
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30 sq cm. Sample reasoning: The two small triangles can be rearranged into a 3-by-3 square (9 sq cm). The two large triangles can be rearranged into a 3-by-7 rectangle (21 sq cm). The combined area is , or 30 sq cm.
Show Sample Response
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The areas is 16 square units. Sample reasoning:
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The rectangle can be decomposed into 1 square of 4 square units and 6 identical right triangles. Two right triangles make a square of 4 square units, so 6 right triangles make 3 squares with a combined area of 12 square units.
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The rectangle can be enclosed by a 6-by-6 square (36 square units). The square creates 2 larger right triangles and 2 smaller ones. The larger triangles can be rearranged to make a 4-by-4 square (16 square units). The smaller triangles make a 2-by-2 square (4 square units). Subtracting the areas of the triangles from the 6-by-6 square gives 16 square units.
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30 sq cm. Sample reasoning: The two small triangles can be rearranged into a 3-by-3 square (9 sq cm). The two large triangles can be rearranged into a 3-by-7 rectangle (21 sq cm). The combined area is , or 30 sq cm.