Lesson 8

Area of Triangles

Problem 1

To find the area of this right triangle, Diego and Jada used different strategies. Diego drew a line through the midpoints of the two longer sides, which decomposes the triangle into a trapezoid and a smaller triangle. He then rearranged the two shapes into a parallelogram.

Jada made a copy of the triangle, rotated it, and lined it up against one side of the original triangle so that the two triangles make a parallelogram.

1. Explain how Diego might use his parallelogram to find the area of the triangle.
2. Explain how Jada might use her parallelogram to find the area of the triangle.

Solution

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Problem 2

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

a.

b.

Solution

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Problem 3

Which of the three triangles has the greatest area? Show your reasoning. If you get stuck, try using what you know about the area of parallelograms.

Solution

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Problem 4

Draw an identical copy of each triangle such that the two copies together form a parallelogram. If you get stuck, consider using tracing paper.

Solution

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(From Unit 1, Lesson 7.)

Problem 5

1. A parallelogram has a base of 3.5 units and a corresponding height of 2 units. What is its area?

2. A parallelogram has a base of 3 units and an area of 1.8 square units. What is the corresponding height for that base?

3. A parallelogram has an area of 20.4 square units. If the height that corresponds to a base is 4 units, what is the base?

Solution

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(From Unit 1, Lesson 6.)