Exploring Rectangles

In this activity, you will explore finding the perimeter and area of rectangles.

  1. In the Gizmotm, click on the RECTANGLE tab. Using the sliders, set Base (b) to 7.0 and Height (h) to 4.0. (To quickly set a value, type a number in the box to the right of the slider and press Enter.)
    1. Which sides of this rectangle are 7.0 units long? Which sides are 4.0 units long? Click on Click to measure lengths and measure the sides, using the Gizmo rulers. (For help using the rulers, click on Gizmo help below the Gizmo.)
    2. The perimeter of this rectangle is the distance around the rectangle. Find the perimeter by adding all the side lengths. What is the perimeter? Click on Show perimeter info to check your answer.
    3. Use your work to make a shortcut method for finding perimeter of a rectangle. What is your method? (Hint: Notice that there are two pairs of sides with the same lengths.)
    4. Drag A, B, C, and D to make other rectangles. Find the perimeter of some of these rectangles. Does your method always work? If not, try again.
    5. What is the perimeter of a rectangle with b = 11.0 m and h = 2.0 m? Use the Gizmo to check your answer.
    6. If you know the perimeter of a rectangle is 15.0 feet and the base is 5.0 feet, how can you find the height? Explain your method and then find the answer.
  2. Turn off Show perimeter info. Set Base (b) to 8.0 and set Height (h) to 2.0.
    1. Which sides of this rectangle have length 8.0 and which sides have length 2.0? Use the rulers to check the lengths.
    2. Turn on Show grid. Count how many grid squares fall inside this rectangle. That is the area of the rectangle. Click on Show area info to check your answer. Turn off Show grid.
    3. A rectangle with base = 8 units and height = 2 units has an area of 16 square units. How can you find the area of a rectangle without counting squares on a grid?
    4. Drag A, B, C, and D to see other rectangles and find the area of some of them. Does your method always work? Use the Gizmo to check.
    5. Use your method to find the area of a rectangle with b = 5.6 cm and h = 11.0 cm. Use the Gizmo to check your answer.
    6. If you know the area of a rectangle is 10.0 square inches and the height is 2.0 inches, how can you find the base? Explain your method and then find the answer.

Exploring Squares

In this activity, you will explore finding the perimeter and the area of a square.

  1. Click on the SQUARE tab. Set Side length (s) to 5.0.
    1. Which sides are 5.0 units long? Why does only one side length need to be given?
    2. The perimeter of this square is the distance around the square. Find the perimeter by adding all the side lengths. What is the perimeter? Click on Show perimeter info to check your answer.
    3. Make a method for finding the perimeter of a square that uses multiplication rather than addition. Use s for side length. What is your method? (Hint: How many sides in a square have the same length?)
    4. Drag A, B, C, and D to make other squares. Test your method by finding the perimeter of some of these squares. Does it always work? If not, try again.
    5. Use your formula to find the perimeter of a square with s = 7.5 cm. What is the perimeter? Check your answer in the Gizmo.
    6. If you know the perimeter of a square is 42 m, find the length of each side. Use the Gizmo to check your answer.
  2. Turn off Show perimeter info. Set Side length (s) to 6.0.
    1. Turn on Show grid. Count how many grid squares fall inside this square. That is the area of the square. Click on Show area info to check your answer. Turn off Show grid.
    2. A square with sides that are 6 units long has an area of 36 square units. How can you find the area of a square without counting grid squares?
    3. Use the method you found in the previous question to find the area of a square with s = 9.0 feet. Check your answer using the Gizmo.
    4. If you know that the perimeter of a square is 28 inches, what is the area of that square? Explain how you found your answer.
    5. If the area of a square is 64 cm2, find the perimeter. Explain your method.