Grade 6 | Unit 1 | Lesson 7: From Parallelograms to Triangles | Practice Problems

Did Clare partition the figure into two identical shapes? Explain your reasoning.

• Yes, the rectangle is 2 units by 4 units, so it has an area of 8 square units. The triangle is half of a 4-by-4 square, so its area is also 8 square units.

• No, although the shapes have the same area, they are not identical shapes—one is a rectangle and the other a triangle.

Triangle R is a right triangle. Can we use two copies of Triangle R to compose a parallelogram that is not a square?

• Yes, we can use two right triangles R to compose a parallelogram that is not a square by joining them along one of the shorter sides (the sides that make the right angle).

• No, we cannot compose such a parallelogram with Triangle R.

Two copies of this triangle are used to compose a parallelogram. Which parallelogram cannot be a result of the composition?

• 
• 
• C

• D

On the grid, draw at least three different quadrilaterals that can each be decomposed into two identical triangles with a single cut.

A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base?