Surface Area of Triangular Prism Worksheet with Answers

10-4 Surface Area of Triangular Prisms Find the surface area of the triangular prism. 2. SOLUTION: area of each triangular base: = 0.48 area of the rectangular faces: 1(1.2) = 1.2 1(1.2) = 1.2 1.2(1.2) = 1.44 Add to find the surface area: 0.48 + 0.48 + 1.2 + 1.2 + 1.44 = 4.8 The surface area is 4.8 square centimeters. ANSWER: 4.8 cm2 4. SOLUTION: area of each triangular base: = 60 area of the rectangular faces: 12(11) = 132 10(11) = 110 15.6(11) = 171.6 Add to find the surface area: 60 + 60 + 132 + 110 + 171.6 = 533.6 The surface area is 533.6 square centimeters. ANSWER: 533.6 cm2 Page 1 10-4 Surface Area of Triangular Prisms 6. A decorative gift box is in the shape of a triangular prism as shown. What is the surface area of the box? SOLUTION: area of each triangular base: = 37.5 area of the rectangular faces: 7.5(5) = 37.5 10(5) = 50 12.5(5) = 62.5 Add to find the surface area. 37.5 + 37.5 + 37.5 + 50 + 62.5 = 225 The surface area is 225 square inches. ANSWER: 225 in2 Page 2 10-4 Surface Area of Triangular Prisms 8. Multiple Representations The figure shows the dimensions of a triangular prism. a. Models Draw a model of the faces and bases of the triangular prism. b. Words Describe the triangular prism. c. Numbers Find the surface area of the triangular prism using addition. SOLUTION: a. b. Sample answer: The prism has right triangle bases each with an area of 24 ft2. The rectangular faces have an area of 72 ft2, 120 ft2, and 96 ft2. The total surface area is 336 ft2. c. 24 + 24 + 72 + 120 + 96 = 336; 336 ft2 ANSWER: a. b. Sample answer: The prism has right triangle bases each with an area of 24 ft2. The rectangular faces have an area of 72 ft2, 120 ft2, and 96 ft2. The total surface area is 336 ft2. c. 24 + 24 + 72 + 120 + 96 = 336; 336 ft2 Page 3 10-4 Surface Area of Triangular Prisms 10. Reason Abstractly Describe the dimensions of a triangular prism that has a surface area between 550 square inches and 700 square inches. SOLUTION: Sample answer: triangular base that measures 9 inches, 12 inches, and 15 inches, and a height of 14 inches ANSWER: Sample answer: triangular base that measures 9 inches, 12 inches, and 15 inches, and a height of 14 inches Page 4 10-4 Surface Area of Triangular Prisms 12. Justify Conclusions Gary is painting a decorative box with the dimensions shown. A can of paint covers about 25 square feet. Does he have enough to paint the lateral surface area of his box with three coats of paint? Justify your answer. SOLUTION: Find the lateral surface area. front rectangle So the area of the front rectangle is 102 in² Side rectangle The area of each side rectangle is 72 in² To find the lateral surface area, find the sum of the areas of all three sides. 102 + 72 + 72 = 246 in² 1 square foot = 144 square inches To convert 244 square inches to square feet, divide by 144 The lateral surface area of the box is 1.7 ft². If you were going paint the area three times, multiply the lateral surface area by three to determine the amount of paint needed. Three coats would need to cover 5.1 ft², which is much less than the 25 ft². ANSWER: yes; Sample answer: The area of the rectangular faces is about 1.7 ft ². Three coats would need to cover 5.1 ft², which is much less than the 25 ft². Page 5 10-4 Surface Area of Triangular Prisms Be Precise Find the surface area of each triangular prism. Round to the nearest tenth if necessary. 14. SOLUTION: area of each base: = 33.9 m2 areas of faces: 11.3 · 9.5 = 107.35 m2 8.5 · 9.5 = 80.75 m2 8 · 9.5 = 76 m2 surface area = 33.9 + 33.9 + 107.35 + 80.75 + 76 or 331.9 m2 ANSWER: 331.9 m2 16. SOLUTION: area of each triangular base: = 30 area of the rectangular faces: 5(16) = 80 12(16) = 192 13(16) = 208 Add to find the surface area: 30 + 30 + 80 + 192 + 208 = 540 The surface area is 540 square feet. ANSWER: 540 ft2 Page 6 10-4 Surface Area of Triangular Prisms 18. SOLUTION: area of each triangular base: = 34.8 area of the rectangular faces: 8.2(12) = 98.4 8.5(12) = 102 11.6(12) = 139.2 Add to find the surface area. 34.8 + 34.8 + 98.4 + 102 + 139.2 = 409.2 The surface area of the prism is 409.2 square meters. ANSWER: 409.2 m2 Page 7 10-4 Surface Area of Triangular Prisms Copy and Solve Find the surface area of the triangular prism using the base triangles shown. Show your work on a separate piece of paper. 20. height of prism: 15 ft SOLUTION: area of each triangular base: = 30 area of the rectangular faces: 5(15) = 75 12(15) = 180 13(15) = 195 Add to find the surface area. 30 + 30 + 75 + 180 + 195 = 510 The surface area is 510 square feet. ANSWER: 510 ft2 Page 8 10-4 Surface Area of Triangular Prisms 22. The attic of the house is a wooden surface. Select values to complete the model below to find how much wood is needed to make the roof of the house and the floor of the attic. How many square meters of wood are needed to build the roof and the floor of the attic? SOLUTION: The total amount of wood needed is 100 + 80 or 180 square meters. . ANSWER: The total amount of wood needed is 100 + 80 or 180 square meters. . Page 9 10-4 Surface Area of Triangular Prisms Identify the triangle as acute, right, or obtuse. 24. SOLUTION: All angles of the triangle are acute, so it is an acute triangle. ANSWER: acute 26. A certain two-dimensional figure has two pairs of parallel lines, four right angles, and four congruent sides. What is the figure? SOLUTION: The only quadrilateral that has two pairs of parallel lines, four right angles, and four congruent sides is a square. ANSWER: square Page 10