10-5 Surface Area of Pyramid

10-5 Surface Area of Pyramids Find the surface area of the pyramid. 2. SOLUTION: area of base: 12(12) = 144 area of each triangular side: (12)(15) = 90 Add to find the surface area. 144 + 90 + 90 + 90 + 90 = 504 square yards ANSWER: 504 yd2 4. SOLUTION: area of base: 5(5) = 25 area of each triangular side: (5)(8.2) = 20.5 Add to find the surface area. 25 + 20.5 +20.5 +20.5 +20.5 = 107 square feet ANSWER: 107 ft2 Page 1 10-5 Surface Area of Pyramids 6. SOLUTION: area of base: (3)(2.6) = 3.9 area of each lateral face: (3)(6) = 9 Add to find the surface area. 3.9 + 9 + 9 + 9 = 30.9 square inches ANSWER: 30.9 in2 8. An earring design is shaped like a triangular pyramid. All sides are equilateral triangles with side lengths of 14 millimeters. The slant height is 12.1 millimeters. What is the surface area of the earring? SOLUTION: Each face has an area of (14)(12.1) or 84.7 square millimeters. So, the surface area of the triangular pyramid is 4 · 84.7 or 338.8 square millimeters. ANSWER: 338.8 mm2 Page 2 10-5 Surface Area of Pyramids 10. Identify Structure Refer to the figures listed in the table. Determine the number of faces the figure has of each two-dimensional shape. Explain. SOLUTION: A rectangular prism is a three-dimensional figure with two parallel bases that are congruent rectangles. Therefore there are 6 rectangular faces. A triangular prism is a prism that has triangular bases. Therefore there are 2 triangular faces and 3 rectangular faces. A pyramid is a three-dimensional figure with at least three lateral faces that are triangles and only one base. Therefore a square pyramid has rectangular face and 4 triangular faces. A triangular pyramid has 4 triangular faces. Sample answer: Rectangular prisms have no triangular faces and triangular pyramids have no rectangular faces. Triangular prisms and square pyramids have a combination of both. The figures are named by their bases. ANSWER: Sample answer: Rectangular prisms have no triangular faces and triangular pyramids have no rectangular faces. Triangular prisms and square pyramids have a combination of both. The figures are named by their bases. Page 3 10-5 Surface Area of Pyramids 12. Persevere with Problems The lateral surface area L.A. of a pyramid is the area of its lateral faces. Use the square pyramid at the right to complete each step to find the lateral surface area of any pyramid. SOLUTION: ANSWER: Find the surface area of the pyramid. 14. SOLUTION: area of base: 5(5) = 25 area of each triangular side: (5)(3) = 7.5 Add to find the surface area. 25 + 7.5 + 7.5 + 7.5 + 7.5 = 55 square meters ANSWER: 55 m2 Page 4 10-5 Surface Area of Pyramids 16. SOLUTION: area of base: 3(3) = 9 area of each triangular side: (3)(6) = 9 Add to find the surface area. 9 + 9 + 9 + 9 + 9 = 45 square yards ANSWER: 45 yd2 18. SOLUTION: area of base: (12)(10.4) = 62.4 area of each lateral face: (12)(12) = 72 Add to find the surface area. 62.4 + 72 + 72 + 72 = 278.4 square meters ANSWER: 278.4 m2 Page 5 10-5 Surface Area of Pyramids 20. A paper model of the Khafre pyramid in Egypt has a square base 7.2 centimeters on each side. The slant height is 6 centimeters. How much paper was used to make the model? SOLUTION: area of base: (7.2)(7.2) = 51.84 area of each triangular side: (7.2)(6) = 21.6 Add to find the surface area. 51.84 + 21.6 + 21.6 + 21.6 + 21.6 = 138.24 square centimeters ANSWER: 138.24 cm2 22. A salt shaker is in the shape of a square pyramid. The perimeter of the base is 16 cm, the height of the salt shaker is 10 cm, and the slant height is about 10.2 cm. Select values to label the net below with the correct dimensions. What is the surface area of the salt shaker. SOLUTION: The length of the slant height is given in the problem, it is 10.2 cm. To find the length of the base, use the perimeter and work backwards. The perimeter of a square is P = 4s, where s is the length of the side. So the length of the base is 4 cm. Next, find the surface area. area of base: 4(4) = 16 area of each triangular side: (4)(10.2) = 20.4 Add to find the surface area. 16 + 20.4 + 20.4 + 20.4 + 20.4 = 97.6 square centimeters Page 6 10-5 Surface Area of Pyramids ANSWER: 97.6 cm² Divide. 24. 240 ÷ 10 = SOLUTION: Cross out the same number of zeros in the dividend and the divisor. So, 240 ÷ 10 is 24. ANSWER: 24 26. 4,800 ÷ 80 = SOLUTION: Use the fact family 6, 8, and 48. So, 4,800 ÷ 80 = 60. ANSWER: 60 Page 7 10-5 Surface Area of Pyramids 28. How many centimeters are equal to 0.05 meters? SOLUTION: Since 1 meter = 100 centimeters, multiply 0.05 by 100. So, 0.05 meters = 5 centimeters ANSWER: 5 cm eSolutions Manual - Powered by Cognero Page 8