Lesson 7
Area of Triangles
Let’s use what we know about parallelograms to find the 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.
 Explain how Diego might use his parallelogram to find the area of the triangle.
 Explain how Jada might use her parallelogram to find the area of the triangle.
Problem 2
Find the area of the triangle. Explain or show your reasoning.
a.
b.
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.
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.
Problem 5

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

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

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?