Lesson 6: Practice Problems

Problem 1

Which three of these parallelograms have the same area as each other?

  1. parallelogram, the top and bottom are each 5 units long, and the sides descend 3 units and move right 1 unit.
  2. parallelogram, the top and bottom are each 3 units long and the left and right sides ascend 5 units while moving right 6 units.
  3. a square of 4 units on each side.
  4. a parallelogram, the left and right sides ascend 3 units, and the top and bottom descend 1 unit as they move right 5 units.

Problem 2

Which of the following pairs of base and height produces the greatest area? All measurements are in centimeters.

  1. ,

  2. ,

  3. ,

  4. ,

Problem 3

Here are the areas of three parallelograms. Use them to find the missing length (labeled with a “?”) on each parallelogram.

  1. 10 square units

    parallelogram with base measure 5 and height unknown.

  2. 21 square units

    parallelogram with height measure 7 and base unknown with extension to rectangle measuring 1

  3. 25 square units

    parallelogram with height measure 5 and base unknown with extension to rectangle measuring 2.5

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 5

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 6 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.