Lesson 5: Practice Problems

Problem 1

List all segments that could represent a corresponding height if the side is the base.

A parallelogram with a bottom side labeled m and a right side labeled n. Dashed lines e, f, j, and k are drawn perpendicular to side m, and dashed lines g and h are drawn perpendicular to side n.

Problem 2

Find the area of each parallelogram.

  1. 2-by-4 rectangle on grid
  2. parallelogram on grid with a horizontal side that is 5 units long and a height for the base 2 units
  3. parallelogram on grid, base is 2 units, and the height for this base is 4 units.

Problem 3

Find the area of each parallelogram.

  1. parallelogram with height 4 cm and base 9 cm
  2. parallelogram with base 5 cm and height 4 cm
  3. parallelogram with base b and height h

Problem 4

The Dockland Building in Hamburg, Germany is shaped like a parallelogram.

The Dockland Building in Hamburg, Germany that is shaped like a parallelogram.

If the length of the building is 86 meters and its height is 55 meters, what is the area of this face of the building?

Problem 5 From Unit 1 Lesson 4

Do you agree with each of these statements? Explain your reasoning.

  1. A parallelogram has six sides.

  2. Opposite sides of a parallelogram are parallel.

  3. A parallelogram can have one pair or two pairs of parallel sides.

  4. All sides of a parallelogram have the same length.

  5. All angles of a parallelogram have the same measure.

Problem 6 From Unit 1 Lesson 2

A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.

  1. What is the area, in square meters, of 6 triangles? If you get stuck, draw a diagram.

  2. How many triangles are needed to compose a region that is square meters?

Problem 7 From Unit 1 Lesson 3

Find the area of the shaded region. All measurements are in centimeters. Show your reasoning.

A shaded rectangle located at an angle within a larger rectangle. The sides of the larger rectangle are divided where the smaller rectangle contacts them. The longer sides are labeled 2 and 12 on each side of the divide, and the shorter sides are labeled 6 and 4 on each side of the divide.