Lesson 2: Practice Problems

Problem 1

The diagonal of a rectangle is shown.

  1. Decompose the rectangle along the diagonal, and recompose the two pieces to make a different shape.

    Blank grid with blue 2x3 rectangle with black diagonal line.

  2. How does the area of this new shape compare to the area of the original rectangle? Explain how you know.

Problem 2

Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of original square to make a new figure.

Two shapes. The first is a square comprised of 16 small squares arranged in four rows of 4. The second image has the center four squares removed and a square added to the outside of each side of the square.

How does the area of her new figure compare with that of the original square?

  1. The area of the new figure is greater.

  2. The two figures have the same area.

  3. The area of the original square is greater.

  4. We don’t know because neither the side length nor the area of the original square is known.

Problem 3

The area of the square is 1 square unit. Two small triangles can be put together to make a square or to make a medium triangle.

Three figures. A square, a small triangle, and a medium triangle.

Which figure also has an area of square units? Select all that apply.

  1. A figure composed of three small triangles
  2. figure composed of three small triangles
  3. figure composed of one medium triangle and one small triangle
  4. figure composed of two small triangles and one square.

Problem 4 From Unit 1 Lesson 1

The area of a rectangular playground is 78 square meters. If the length of the playground is 13 meters, what is its width?

Problem 5 From Unit 1 Lesson 1

A student said, “We can’t find the area of the shaded region because the shape has many different measurements, instead of just a length and a width that we could multiply.”

A multi-sided figure. The sides on top measure 10 units, 35 units, and 15 units. Two of the three sides on the left measure 10 units. One of the two sides on the right measures 10 units. One of the two sides on the bottom measure 15 units. The total width of the figure is 60 units, and the total height is 30 units. All angles are right angles.

Explain why the student’s statement about area is incorrect.