Finding the Area of a Rectangle

Plot the vertices (-4, -4), (-2, 1), and (5, 1). To form a parallelogram, plot the last vertex at point _______ The area of the parallelogram is _____ square units.

(3, -4) 35

Patty has decided to redecorate her room with parallelograms. She finds a piece of fabric with a parallelogram design and makes a tapestry to hang on the wall. The tapestry is a parallelogram with a base of 3 feet and a height of 4 feet. Parallelogram What is the area of the tapestry?

12 ft squared

Mateo has 60 wooden tiles in the shape of diamonds as shown below. He plans to glue these tiles side by side onto a tabletop. What will the area of the tabletop be?

1620 in squared

Patty has a bulletin board on her wall with the dimensions shown. How many photos in the shape of a parallelogram will it take to cover the bulletin board if each photo has a base of 6 inches and a height of 4 inches?

36 Photos

Leo has 100 paving tiles in the shape of parallelograms as shown below. He plans to make a patio using these tiles. What will the area of the patio be?

3600 in squared

Seth wants to cover the top of a small table with glass parallelogram tiles. The top of the table measures 18 inches by 14 inches. If each tile has four sides of length 3 inches with a height of 2 inches, about how many tiles will he need?

42

Patty lives in Tennessee, and has figured out she can use a parallelogram to estimate the state's area. Estimate the area of Tennessee if the base of the parallelogram is 440 miles and the height is 100 miles. What is the estimated area of Tennessee?

44,000 square miles

If the height and base of the parallelogram shown are each decreased by 2 cm, what is the area of the new parallelogram?

48 cm squared

Lorea is designing the top of a quilt which measures 2,160 square inches. Triangles will cover 432 square inches of the quilt, and squares will cover 180 square inches. The rest of the quilt will be parallelograms with a base of 2 inches and a height of 1.5 inches. How many parallelograms should she cut to complete the quilt?

516

If the height of the parallelogram shown is increased by 1 cm and the base is increased by 2 cm, what is the area of the new parallelogram?

55 cm ssquared

Mr. Lee wants to make a seating area in his backyard. He outlines a parallelogram-shaped area. The drawing shows the dimensions. Which formula shows how to find the area of the seating area?

A = (14 ft)(10 ft)

Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to find the area of lawn that remains. Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?

He is incorrect. The path will have an area of mc022-2.jpg sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.

Patty made a name tag in the shape of a parallelogram. Reilly made a rectangular name tag with the same base and height. Explain how the areas of the name tags compare.

Sample response: A parallelogram can be transformed into a rectangle with the same base and height. So, the area of a parallelogram and a rectangle with the same base and height will have the same area. Both shapes use the formula A = bh to find the area.

Patty has a parallelogram that has a base of 3 feet and a height of 5 feet. The base and height will each be doubled. Will the area also be doubled? Explain how you know.

Sample response: No, the area will be multiplied by 4. The original area is 3 × 5 = 15 square feet. If the base and the height are both doubled, then the new area will be 6 × 10 = 60. 60 is 4 times 15.

The top of a table is a parallelogram with a base of 28 cm and a height of 20 cm. Patty wants to cover the table with tiles that have an area of 8 cm2 each. Jake wants to use tiles that have an area of 9 cm2 each. How many more tiles will Patty need than Jake to cover the table? Explain your answer

Sample response: The area of the top of the table is 28 × 20 = 560 cm2. The area of Patty's tiles is 8 cm2 each and the area of Jake's tiles is 9 cm2 each. Patty will need 560 ÷ 8, or 70, tiles. Jake will need 560 ÷ 9, or about 63, tiles. So, Patty will use about 7 more tiles.

The top of a table is a parallelogram with a base of 28 cm and a height of 20 cm. Patty wants to cover the table with tiles that have an area of 8 cm2 each. Jake wants to use tiles that have an area of 9 cm2 each. How many more tiles will Patty need than Jake to cover the table? Explain your answer.

Sample response: The area of the top of the table is 28 × 20 = 560 cm2. The area of Patty's tiles is 8 cm2 each and the area of Jake's tiles is 9 cm2 each. Patty will need 560 ÷ 8, or 70, tiles. Jake will need 560 ÷ 9, or about 63, tiles. So, Patty will use about 7 more tiles.

A parallelogram-shaped tapestry has a base of 6 feet and a height of 5 feet. Explain how you would find the area of the tapestry. What is the area?

Sample response: Use the formula A = bh. Multiply the base times the height: 6 × 5 = 30. The area of the tapestry is 30 square feet.

Patty buys a carpet that is made up of 9 parallelograms. Each parallelogram has a base of 12 inches and a height of 20 inches.

The area of each parallelogram is 240 square inches. The area of the carpet is 2160 square inches.

Mr. Lee wants to make a seating area in his backyard. He outlines a parallelogram-shaped area. The drawing shows the dimensions. Use the figure to complete the statements.

The area of the parallelogram is 120 ft2. Mr. Lee wants to cover the seating area with tiles. If each tile has an area of 4 ft2, he will need 30 tiles to cover the seating area.

Mandy cut a parallelogram to make a rectangle. Parallelograms and Rectangles She then used the formula A = bh to find the area of the rectangle. A = bh A = (5)(3) A = 15 square units Which is true about the area of the parallelogram?

The area of the parallelogram is equal to 15 units squared.

Use the figure to complete the statements.

The base (b) of the parallelogram is 16 feet. The height (h) of the parallelogram is 10 feet. The area of the parallelogram is 160 square feet.

Which statement is correct regarding the measurements of the parallelogram?

The base is 8 and the height is 3, so the area is 8(3) = 24 square units.

The parallelogram has vertices at (-2, 2), (4, 2), (1, -2), and (-5, -2). Complete each sentence.

The base of the parallelogram is 6 units. The height of the parallelogram is 4 units. The area of the parallelogram is 24 square units

Complete each sentence using the rectangle graphed on the coordinate plane.

The length of the rectangle is 7 units. The width of the rectangle is 3 units. The area of the rectangle is 21 square units.`