Covering and Surrounding Assessment. 1. (1 point) Find the area and perimeter of this rectangle. Explain how you found your answers.

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1 Name: Date: Score: /20 Covering and Surrounding Assessment Short Answer: Answer each question, making sure to show your work or provide an explanation or sketch to support your answer in the box. Make sure to include the correct units when it is appropriate to do so. 1. (1 point) Find the area and perimeter of this rectangle. Explain how you found your answers. 2. (1 point) Angela has sketched a rectangle. She says that the sum of the sides of the rectangle is 26 cm, and the length of one side is 7 cm. What are the length and width of Angela s rectangle? Explain how you found your answer.

2 3. Hau was using cardboard to make mats for her photos. The photos were 3 inches by 4 inches. The mats were different sizes and different shapes. a. (1 point) How much cardboard (in square inches) will be showing in the rectangular mat? b. (1 point) How much cardboard (in square inches) will be showing in the non-rectangular mat? c. (2 points) If she decided to put a narrow frame around each mat, how many inches of frame material would she need to surround each of the mats? 4. (2 points) In the diagram on the right, the squares on the grid are 1 centimeter long and 1

3 centimeter wide. Find the area and perimeter of the figure. Explain your reasoning and any strategies that you use. 5. Chad's dad wants to repaint the top of the step outside the front door with special paint that doesn't get slippery in the rain. Below is the drawing of the top of the step. Each centimeter represents 1 foot. a. (1 point) Using the scale drawing, help Chad's dad by finding the area of the step. Keep a record of your work and sketches so you can convince him that you found it correctly. b. (1 point) Each quart of paint covers 32 square feet. Chad's dad wants to apply two coats of paint. How many quarts of paint should he buy? Explain your answer.

4 6. (2 points) Find the area and perimeter of the triangle on the right. Show your work. 7. (3 points) Find the radius, diameter and circumference of the circle.

5 Multiple Choice: Identify the choice that best completes the statement or answers the question. Show your work or provide an explanation for your answer in the box provided. 8. (1 point) What is the area of this triangle? a. 18 sq. m b. 36 sq. m c. 9 sq. m d. 6 sq. m 9. (1 point) Alexa wants to use ready-made 6-foot long fence sections for her yard. The yard is a rectangle with dimensions 30 feet by 36 feet. How many fence sections will she need to enclose her entire yard?

6 a. 22 b. 132 c. 66 d (1 point) The figure below shows the dimensions of Aman s bedroom. Aman wants to put new carpet in the room. Which of the following will help him figure out how much carpet he needs? a. (6 10) + (2 3) c b d. (6 3) + (2 3) (1 point) If the width of a rectangle is tripled, what will be the effect on its area? a. The area will remain the same. c. The area will be 3 times as great. b. The area will be 9 times as great. d. The area will be 6 times as great. 12. (1 point)

7 What is the relationship between the area of the triangle and the area of the rectangle below? a. The area of the triangle is the same as the area of the rectangle. b. The area of the triangle is half the area of the rectangle. c. The area of the triangle is twice the area of the rectangle. d. The area of the triangle is one-third the area of the rectangle. 13. (1 point) Which two figures below have the same area? a. Figures I and II c. Figures II and IV b. Figures II and III d. Figures I and IV

8 Bits and Pieces I Unit Test Answer Section SHORT ANSWER 1. ANS: Answers will vary. Possible answers: PTS: 1 DIF: L2 REF: Covering and Surrounding Check-Up OBJ: Investigation 1: Designing Bumper Cars NAT: NAEP M1h NAEP M2b NAEP M2f TOP: Problem 1.2 Finding Area and Perimeter of Rectangles KEY: area of a rectangle area and perimeter perimeter 2. ANS: Area: 20 sq. cm, Perimeter: 18 cm; Possible explanation: I multiplied 5 by 4 to find the area. To find the perimeter I added the length and the width, then multiplied this answer by 2, in order to account for both lengths and both widths. PTS: 1 DIF: L2 REF: Covering and Surrounding Check-Up OBJ: Investigation 1: Designing Bumper Cars NAT: NAEP M1h NAEP M2b NAEP M2f TOP: Problem 1.2 Finding Area and Perimeter of Rectangles KEY: dimension area of a rectangle perimeter 3. ANS: a. 18 sq. in. (The mat is 30 sq. in. while the photo is 12 sq. in.) b. 16 sq. in. (The mat is 28 sq. in. while the photo is 12 sq. in.) c. The rectangular mat will require 22 in of frame materials. The non-rectangular mat will require 24 in. PTS: 4 DIF: L2 REF: Covering and Surrounding Partner Quiz OBJ: Investigation 1: Designing Bumper Cars Investigation 4: Measuring Parallelograms NAT: NAEP M1h NAEP M2b NAEP M2f NAEP M2a NAEP M2d NAEP G3f TOP: Problem 1.1 Understanding Area and Perimeter Problem 4.1 Finding Measures of Parallelograms KEY: area, perimeter base, height 4. ANS: 42 square centimeters. Possible explanation: We cut the shape into a 5 by 6 rectangle and two triangles, each with base 4 centimeters and height 3 centimetrs. The area of the figure is the sum of the areas of these smaller shapes: = 42. PTS: 1 DIF: L2 REF: Covering and Surrounding Partner Quiz OBJ: Investigation 1: Designing Bumper Cars NAT: NAEP M1h NAEP M2b NAEP M2f TOP: Problem 1.1 Understanding Area and Perimeter KEY: area perimeter 5. ANS: a. Some students may know that the formula for the area of a trapezoid is and calculate = 8 square feet. Others may divide the trapezoid into a rectangle and two triangles, where the area of the rectangle is 3 2 = 6 square feet and the area of each congruent triangle is = 1 square foot for a total of = 8 square feet.

9 b. For two coats he needs to cover 8 2 = 16 square feet. A quart covers 32 square feet, and 16 is half of 32, so half a quart of paint is needed. If you can't buy the paint in half quarts, 1 quart would be needed. PTS: 2 DIF: L2 REF: Covering and Surrounding Question Bank OBJ: Investigation 4: Measuring Parallelograms NAT: NAEP M2a NAEP M2d NAEP G3f TOP: Problem 4.1 Finding Measures of Parallelograms KEY: base height area of a trapezoid 6. ANS: a. P = 15.4 cm, A = 10 sq. cm b. P = 13 cm, A = 7.5 sq. cm c. P = 19.8 cm, A = 17.5 sq. cm d. P = 22.2 cm, A = 10 sq. cm PTS: 2 DIF: L2 REF: Covering and Surrounding Additional Practice Investigation 3 OBJ: Investigation 3: Measuring Triangles NAT: NAEP G5a NAEP M2a NAEP M1h TOP: Problem 3.1 Finding Area and Perimeter of Triangles KEY: base height area of a triangle perimeter 7. ANS: a. r = 3 ft; d = 6 ft C = ft PTS: 3 DIF: L2 REF: Covering and Surrounding Additional Practice Investigation 5 OBJ: Investigation 5: Measuring Irregular Shapes and Circles NAT: NAEP M1b NAEP M1C NAEP M1g TOP: Problem 5.2 Finding Circumference Problem 5.3 Exploring Area and Circumference KEY: center diameter radius circumference pi area of a circle MULTIPLE CHOICE 8. ANS: C PTS: 1 DIF: L2 OBJ: Investigation 3: Measuring Triangles NAT: NAEP G5a NAEP M2a NAEP M1h TOP: Problem 3.1 Finding Area and Perimeter of Triangles KEY: base height area of a triangle 9. ANS: A PTS: 1 DIF: L2 OBJ: Investigation 2: Changing Area Changing Perimeter NAT: NAEP G1d NAEP G2d NAEP M2f TOP: Problem 2.3 Constant Perimeter Changing Area KEY: perimeter dimensions 10. ANS: C PTS: 1 DIF: L2 OBJ: Investigation 1: Designing Bumper Cars NAT: NAEP M1h NAEP M2b NAEP M2f TOP: Problem 1.2 Finding Area and Perimeter of Rectangles KEY: dimension area area of a rectangle angle 11. ANS: A PTS: 1 DIF: L2 OBJ: Investigation 2: Changing Area Changing Perimeter NAT: NAEP G1d NAEP G2d NAEP M2f

10 TOP: Problem 2.2 Perimeters and Irregular Shapes KEY: area area of an irregular figure 12. ANS: B PTS: 1 DIF: L2 OBJ: Investigation 3: Measuring Triangles NAT: NAEP G5a NAEP M2a NAEP M1h TOP: Problem 3.1 Finding Area and Perimeter of Triangles KEY: base height area of a rectangle area of a triangle 13. ANS: B PTS: 1 DIF: L2 OBJ: Investigation 3: Measuring Triangles NAT: NAEP G5a NAEP M2a NAEP M1h TOP: Problem 3.2 Identifying Base and Height KEY: area of a triangle base height

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