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Lateral Area of a Regular Pyramid Find the lateral area of the square pyramid. Lateral area of a regular pyramid P = 2.5 ● 4 or 10, ℓ = 5 Answer: The lateral area is 25 square centimeters. Find the lateral area of the square pyramid. A. 54 in2 B. 64 in2 C. 108 in2 D. 132 in2 Surface Area of a Square Pyramid Find the surface area of the square pyramid to the nearest tenth. Step 1 Find the slant height c2 = a2 + b2 Pythagorean Theorem ℓ2 = 62 + 42 a = 6, b = 4, and c = ℓ ℓ= Simplify. Surface Area of a Square Pyramid Step 2 Find the perimeter and area of the base. P = 4 ● 8 or 32 m Step 3 Find the surface area of the pyramid. __ S = 1 Pℓ + B 2 1 (32) = __ 2 ≈ 179.4 A = 82 or 64 m2 Surface area of a regular pyramid + 64 P = 32, ℓ = , B = 64 Use a calculator. Answer: The surface area of the pyramid is about 179.4 square meters. Find the surface area of the square pyramid to the nearest tenth. A. 96 in2 B. 124.3 in2 C. 138.5 in2 D. 156 in2 Surface Area of a Regular Pyramid Find the surface area of the regular pyramid. Round to the nearest tenth. Step 1 Find the perimeter of the base. P = 6 ● 10.4 or 62.4 cm Surface Area of a Regular Pyramid Step 2 Find the length of the apothem and the area of the base. 360° or A central angle of the hexagon is ______ 6 60°, so the angle formed in the triangle is 30°. Surface Area of a Regular Pyramid tan 30° = Write a trigonometric ratio to find the apothem a. a= Solve for a. a ≈ 9.0 Use a calculator. A= Area of a regular polygon ≈ Pa (62.4)(9.0) Replace P with 62.4 and a width 9.0. ≈ 280.8 Multiply. So, the area of the base is approximately 280.8 cm2. Surface Area of a Regular Pyramid Step 3 Find the surface area of the pyramid. S= ≈ Pℓ + B Surface area of regular pyramid (62.4)(15) + 280.8 P = 62.4, ℓ = 15, and B ≈ 280.8 ≈ 748.8 Simplify. Answer: The surface area of the pyramid is about 748.8 cm2. Find the surface area of the regular pyramid. Round to the nearest tenth. A. 198 in2 B. 228.5 in2 C. 255.5 in2 D. 316.3 in2 Lateral Area of a Cone ICE CREAM A sugar cone has an altitude of 8 inches and a diameter of inches. Find the lateral area of the sugar cone. If the cone has a diameter of radius then the Use the altitude and the radius to find the slant height with the Pythagorean Theorem. Lateral Area of a Cone Step 1 Find the slant height ℓ. ℓ2 = 82 + 1.252 Pythagorean Theorem ℓ2 ≈ 65.56 Simplify. ℓ ≈ 8.1 Step 2 Take the square root of each side. Find the lateral area L. L = rℓ Lateral area of a cone ≈ (1.25)(8.1) r = 1.25 and ℓ ≈ 8.1 ≈ 31.8 Answer: The lateral area of the sugar cone is about 31.8 square inches. HATS A conical birthday hat has an altitude of 6 inches and a diameter of 4 inches. Find the lateral area of the birthday hat. A. 39.7 in.2 B. 43.6 in.2 C. 48.2 in.2 D. 53.1 in.2 Surface Area of a Cone Find the surface area of the cone. Round to the nearest tenth. Estimate: S ≈ 3 ● 1.5 ● 3 + 3 ● 2 or 19.5 cm2 S = rℓ + r2 Surface area of a cone = (1.4)(3.2) + (1.4)2 r = 1.4 and ℓ = 3.2 ≈ 20.2 Answer: The surface area of the cone is about 20.2 square centimeters. This is close to the estimate, so the answer is reasonable. Find the surface area of the cone. Round to the nearest tenth. A. 58.2 cm2 B. 61.3 cm2 C. 63.6 cm2 D. 70.7 cm2