Area: Shapes with Fractional Side Lengths

Triangle Area Formula

A = 1/2bh

Rectangle or Parallelogram

A = bh

Square Area Formula

A = bh or A = s2

The irregular shape can be broken into a triangle and a rectangle as shown. Which expression could be used to determine its area? (10)(4.2) + (0.5)(10)(3.2) (0.5)(10)(4.2) + (10)(3.2) (0.5)(10)(7.4) + (10)(3.2) (10)(7.4) + (0.5)(10)(3.2)

(0.5)(10)(4.2) + (10)(3.2)

Which expression could be used to determine the area of the square? (2)(10.75) (4)(10.75) (10.75)2 (10.75)4

(10.75)2

Gabriel started to calculate the area of the triangle. His work is shown. A = 1/2 bh =1/2 (1/2) (3/4) What is the area of the triangle? The area of the triangle is ___ in.².

3/16

What is the area of the figure? 26.8 square meters 38.8 square meters 43.2 square meters 50.8 square meters

38.8 square meters

What is the area of the figure? Answer in decimal form to the nearest hundredth.

41.25m2

What is the area of a square that has a side length of 2.8 inches? ____ square inches

7.84

How can you break up the figure into familiar shapes to determine the area? Break up the figure into a 2 ft by 3 2/3 ft triangle and a 5 ft by 1/3 ft rectangle. Break up the figure into a 2 ft by 5 ft triangle and a 5 ft by 1/3 ft rectangle. Break up the figure into a 2 ft by 1/3 ft triangle and a 5 ft by 1/3 ft rectangle. Break up the figure into a 2 ft by 1/3 ft triangle and a 5 ft by 1/3 ft rectangle.

Break up the figure into a 2 ft by 3 2/3 ft triangle and a 5 ft by 1/3 ft rectangle.

Magda saw a triangular sign with a base of 4 feet and a height of 2.8 feet. She reasoned that if she first divided each dimension by 2 before multiplying them together, she would get the right area. Is she correct? Explain.

Sample Response: No, Magda is incorrect. The actual area is 0.5(4)(2.8) = 5.6 ft2. With Magda's method, the area would be (2)(1.4) = 2.8 ft2.

What statements are true about the area of the parallelogram? Select all that apply. The area can be found using the formula A =bh The area can be found using the formula A = 1/2bh The area can be found using the formula A=s2 The area is 9.7 m2. The area is 21.96 m2.

The area can be found using the formula A =bh The area is 21.96 m2.

A border for a decorative mirror is made with 20 triangular tiles. Each tile has a base of 0.5 cm and a height of 3 cm. What is the total area of the border? 0.75 cm2 1.5 cm2 15 cm2 30 cm2

15 cm2

The area of a rectangular baking sheet is 25 square inches. The base of the sheet is 10 inches. What is the height? 2 1/2 in. 3 in. 3 1/2 in. 250 in.

2 1/2 in.

What is the area of a rectangle with a base of 12 mm and a height of 1.4 mm? 13.4 mm2 16.8 mm2 134 mm2 168 mm2

16.8 mm2

The irregular figure can be broken into a triangle and a rectangle as shown with the dashed line. The length of b, the base of the triangle, is ____ft. The area of the triangle is ___ ft2. The area of the rectangle is ___ ft2. The area of the irregular figure is ___ ft2.

2 2/3 4 6 2/3 10 2/3

Which expression could be used to determine the area of a rectangle with a length of 3.5 cm and a width of 0.25 cm? 3 + 0.5 + 0.25 3.5 + 0.25 (3.5)(0.25) (3)(0.5)(0.25)

(3.5)(0.25)

Which expression could be used to determine the area of the triangle shown?

1/2 (12 1/3)(3)

Calculating the Area of a Rectangle with a Fractional Dimension What is the area of the rectangle? 9 1/2m2 15 m2 17 1/2m2 19 m2

15 m2

What is the area of the figure? -25 1/6 yd2 22 1/6 yd2 25 1/6 yd2 61 5/6 yd2

25 1/6 yd2

Students are making finger puppets for a puppet show. The figure shown is used as a pattern for a puppet's shirt. What is the area of the pattern? The area is ____square inches.

3

If the base of the triangle decreased from 2 yards to 1 yard, what would be the difference in the area? 1/16 yd2 5/16 yd2 5/8 yd2 1 yd2

5/16 yd2

What is the area of the parallelogram? ___ cm2

8.4

Stefan's neighborhood has a community garden. The garden has 15 equally sized rectangular plots for people to grow fruits and vegetables. Each rectangular plot measures 8 feet by 10 2/5 feet. What is the area of each plot? Of the garden? The area of each plot is___ ft2. The total area of the garden is _____ft2.

83 1/5 1248

How can you break up the figure into familiar shapes to determine the area? Break up the figure into a 4 m by 5.2 m rectangle and a 3 m by 6 m rectangle. Break up the figure into a 4 m by 8.2 m rectangle and a 3 m by 6 m rectangle. Break up the figure into a 4 m by 5.2 m rectangle and a 3 m by 2 m rectangle. Break up the figure into a 4 m by 8.2 m rectangle and a 5.2 m by 2 m rectangle.

Break up the figure into a 4 m by 5.2 m rectangle and a 3 m by 6 m rectangle.

What is the area of the figure? Explain the steps you take to calculate the area

Sample Response: The area is the sum of the square area and the triangle area. The area of the square is A = s2 = 22 = 4 in.2. The base of the triangle is found by subtracting: 3.6 - 2 = 1.6 in. The area of the triangle is A = 1/2 bh=1/2(2)(1.6) = 1.6 in.2. Add the areas to get the total area of the figure: 4 + 1.6 = 5.6 in.2.

Anna calculated the area of parallelogram with a base of 7 2/5m and a height of 2m. Her work is shown here. What errors did the student make? Select all that apply. She used the incorrect area formula. She substitute the values for the base and height incorrectly. She converted the mixed number to an improper fraction incorrectly. She multiplied incorrectly. She simplified the fraction 70/10 incorrectly.

She used the incorrect area formula. She converted the mixed number to an improper fraction incorrectly.

Which statements are true about the area of the square? Select all that apply. The area can be found using the formula A = 1/2bh The area can be found using the formula A = s2 The area is 6.2 mm2. The area is 9.61 mm2. The area is 12.4 mm2.

The area can be found using the formula A = s2 The area is 9.61 mm2.