Section C Section C Checkpoint

Problem 1

Identify a base and a height that you can use to find the area of each triangle. (You don’t have to actually find the areas.)

  • Label each base with “b.”
  • Draw a segment for each height and label it with “h.”

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Solution

Sample response:

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Sample Response

Sample response:

Problem 2

Find the area of the triangle. Explain or show your reasoning.

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Solution

84 square inches. Sample reasoning: If the side that is 14 inches long is the base, its corresponding height is 12 inches. 12⋅14⋅12=12⋅168=84\frac{1}{2} \boldcdot 14 \boldcdot 12 = \frac{1}{2} \boldcdot 168 = 84

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Sample Response

84 square inches. Sample reasoning: If the side that is 14 inches long is the base, its corresponding height is 12 inches. 12⋅14⋅12=12⋅168=84\frac{1}{2} \boldcdot 14 \boldcdot 12 = \frac{1}{2} \boldcdot 168 = 84

Problem 3

Find the area of the shaded polygon in square units. Show your reasoning.

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Solution
15 square units. Sample reasoning:
  • The polygon can be decomposed into two right triangles. 
  • The area of the small triangle is half of a 3-by-2 rectangle, which is 3 square units. The area of the large triangle is half of a 6-by-4 rectangle, which is 12 square units. 3+12=153 + 12 = 15

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Sample Response
15 square units. Sample reasoning:
  • The polygon can be decomposed into two right triangles. 
  • The area of the small triangle is half of a 3-by-2 rectangle, which is 3 square units. The area of the large triangle is half of a 6-by-4 rectangle, which is 12 square units. 3+12=153 + 12 = 15