STAAR Category 3 Grade 7 Mathematics TEKS 7.9D. Student Activity 1
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1 Student Activity 1 Work with your partner to answer the following questions. Problem 1: A triangular prism has lateral faces and faces called bases. The bases are in the shape of a. The lateral faces are in the shape of a. The total surface area of a rectangular prism is the sum of the of the faces. The lateral surface area is the surface area decreased by the area of the bases. The lateral surface area will be the sum of the 3 faces. Problem 2: Look at the net of the triangular prism shown below. areas of the prism. Find the lateral and total surface 17.6 units 24 units 18 units 20 units units The lateral surface area will be the sum of the areas of the three. Rectangle 1 has dimensions of by and will have an area of sq. units. Rectangle 2 has dimensions of by and will have an area of sq. units. Rectangle 3 has dimensions of by and will have an area of sq. units. The lateral surface area is the sum of,, and. The lateral surface area is square units. The total surface area will be the sum of the surface area and the areas of the bases. The area of a base will be 0.5 square units. The area of one base will be square units. The area of the two bases will be 2 or square units. The total surface area will be + or square units. TEKSING TOWARD STAAR 2014 Page 1
2 Problem 3: A box is in the shape of a triangular prism. Find the total surface area of the box by drawing a net and find the areas of the shapes in the net. 15 in. 6 in. 10 in. 8 in. Draw and label the net for the prism. The area of the three rectangular faces will be,, and square inches. The area of each base will be square inches. The area of the two bases will be square inches. The total surface area of the prism is the of the 2 and surface area. Total surface area is in. 2 + in. 2 = in. 2 The total surface area of the box is square inches. Problem 4: Explain the relationship between the sides of the triangular base of a prism and the lateral surface area. If the base of a triangular prism has side lengths of 5, 6, and 8 units and the prism has a height of 10 units, what will be the lateral surface area of the prism? TEKSING TOWARD STAAR 2014 Page 2
3 Problem 5: A rectangular prism has a square base with side lengths of 8 inches and a height of 12 inches. A triangular prism has an equilateral triangle base with side lengths of 8 inches and a height of 12 inches. Compare the lateral surface area of the two prisms. Problem 6: Draw a net for a triangular prism with a height of 20 units. The base is a right triangle with side lengths of 5, 12, and 13 units. Find the total surface area of the prism. Find the lateral surface area of the prism. Problem 7: Design a triangular prism whose lateral surface area is 120 square units. TEKSING TOWARD STAAR 2014 Page 3
4 Student Activity 2 Work with your partner to answer the following questions. Problem 1: Describe the faces of a triangular pyramid. What is the formula for the area of a triangle? For a right triangle, if one leg is considered to be the base, what will be the height of the triangle? Problem 2: Benny made the statement: Every triangle has 3 heights. If that is true, how do you decide which one to use for the area formula? Problem 3: Each square of the grid is 1 square inch. Answer the following questions about the triangular pyramid shown on the grid. Each face is an equilateral triangle with a side length of inches. The height of each triangle is approximately 4.3 inches. C The area of the base is or square inches. Since all four triangles are congruent, then the lateral surface area of the pyramid is three times the area of triangle which is 3 or square inches. The total surface area of the pyramid is the lateral area plus the area of the base. This is + square inches. The total surface area of the pyramid is square inches. TEKSING TOWARD STAAR 2014 Page 4
5 Problem 4: Draw and label a net for the triangular pyramid described below. Find the total and lateral areas for the pyramid using the net. 1. The base is a right triangle with side lengths of 6, 8, and 10 units. The heights of the lateral faces are: 8.9, 8.5, and 8 units. (The shorter the base of the lateral face the longer the height will be.) Net: Find the lateral area of the pyramid. Show your work. Find the total area of the pyramid. Show your work. Problem 5: The base and the three lateral faces of a triangular pyramid are shown below. 18 units 33.3 units 31.3 units 33.1 units 28 units 28 units 30 units 18 units 33.3 units TEKSING TOWARD STAAR 2014 Page 5
6 Find the lateral surface area of the pyramid. Find the total surface area of the pyramid. Problem 6: A pyramid with an equilateral triangular base has a slant height of 14 meters. Each side of the base is 12 meters long. What is the lateral and total surface area of the pyramid? 14 m 12 m Find the lateral surface area: Find the total surface area: TEKSING TOWARD STAAR 2014 Page 6
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9 Student Activity 3 Problems: NETS AND SURFACE AREA How can you use the net needed to represent the surface area of a prism? How can you use the net needed to represent the surface area of a pyramid? Materials: 1 copy of the nets for a triangular prism and a equilateral triangular pyramid per pair of students, 1 metric ruler per pair, 2 pair of scissors, 1 glue stick Procedure: Work in groups of 2 for this activity. Identify Student 1 and Student 2. Part I: Use the net of the prism for Part I. Student 1 will measure the length of the base of the prism using the metric ruler. Record the measurement in centimeters. The length of the base of the prism is cm. Label this measurement on the net. Student 2 will measure the height of the base of the prism in centimeters. The height of the base of the prism is cm. Label this measurement on the net. Calculate the area of the base of the prism. The formula to calculate the area of a triangle is The area of both bases of the prism will be square centimeters. What are the shapes of the lateral faces? Student 1 will measure the height of the prism. The height of the prism is cm. Student 2 will measure any other dimension needed to find the area of the rectangular faces. Calculate the lateral area of the prism. The total surface area of the prism is the sum of and or sq centimeters. Student 1 cuts out the net of the prism. Together work to fold the edges and using a glue stick on the tabs, create the prism from the net. TEKSING TOWARD STAAR 2014 Page 9
10 Part II: Use the net for the equilateral triangular pyramid for Part II. Student 2 will measure the length of the base of the pyramid using the metric ruler. Record the measurement in centimeters. The length of the base of the pyramid is cm. Label this measurement on the net. Student 2 will measure the height of the base of the pyramid in centimeters. The height of the base of the pyramid is cm. Label this measurement on the net. Since the pyramid is an equilateral pyramid, all the faces are. The area of each lateral face is the same as the area of the. Calculate the area of the base of the pyramid. The formula to calculate the area of a triangle is Calculate the lateral area of the pyramid. The total surface area of the pyramid is 4 times the area of triangle. The total surface area of the pyramid is sq centimeters. Student 2 cuts out the net of the pyramid. Together work to fold the edges and using a glue stick on the tabs, create the pyramid from the net. Part III: Suppose the base of a triangular pyramid is a right triangle with side lengths of 2.5, 6, and 6.5 cm. Sketch the triangle below. Use your metric ruler to measure the sides. On the 6 cm side, draw an isosceles triangle with 3 cm height. On the 2.5 cm side, draw an isosceles triangle with a height of 3.4 cm, and on the 6.5 cm side draw an isosceles triangle with a height of 2.7 cm. Calculate the lateral and total surface area of the pyramid using the net you drew. TEKSING TOWARD STAAR 2014 Page 10
11 NAME DATE SCORE /5 7.9D Skills and Concepts Homework 1 1. What information do you need to find the total surface area of a triangular prism? 2. The figure below is a net of a triangular prism. The height of the prism is in. The height of the base of the prism is in. What is the total surface area of the triangular prism? Show your work. 16 in. 16 in. 16 in. 18 in. 13 in. 16 in. 3. The lateral faces of a triangular prism have dimensions of 15 by 12 inches, 18 by 12 inches, and 20 by 12 inches. The area of a base of the prism is 130 square inches. What is the lateral surface area of the prism? What is the total surface area of the prism? TEKSING TOWARD STAAR 2014 Page 11
12 4. A base and the lateral faces of a triangular prism are shown below. Show your work. 18 mm 18 mm 18 mm 25 mm 22 mm 23 mm 25 mm 23 mm 13 mm 13 mm What is the height of the prism? What is the area of a base of the prism? What is the lateral surface area of the prism? What is the total surface area of the prism? 5. A base and the lateral faces of a triangular prism are shown below. Show your work. 16 mm 16 mm 16 mm 34 mm 30 mm 29 mm 34 mm 30 mm 13 mm 20 mm What is the height of the prism? What is the area of a base of the prism? What is the lateral surface area of the prism? What is the total surface area of the prism? TEKSING TOWARD STAAR 2014 Page 12
13 NAME DATE SCORE /5 1. Describe the faces of a triangular pyramid. 7.9D Skills and Concepts Homework 2 2. All the faces of a triangular pyramid are congruent equilateral triangles. One of the triangles is shown below. Each side of the triangle is 5 inches. The height of the triangle is 4.3 inches. What is the lateral surface area of the pyramid? What is the total surface area of the pyramid? 3. A triangular pyramid has a base that is a right triangle with side lengths of 12, 16, and 20 units. The base and the lateral faces are shown below What is the area of the base of the pyramid? TEKSING TOWARD STAAR 2014 Page 13
14 4. What is the lateral surface area of the pyramid in Question 3? What is the total surface area of the pyramid in Question 3? 5. The base and the three lateral faces of a triangular pyramid are shown below. 53 units 40 units 35 units 56 units 50 units 50 units 35 units 55 units 40 units Create a net for the pyramid from the information above. Find the total and lateral surface areas of the pyramid. TEKSING TOWARD STAAR 2014 Page 14
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