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Lesson Menu Five-Minute Check (over Lesson 12–6) Then/Now New Vocabulary Key Concept:Lateral and Surface Area of Pyramids Example 1: Surface Area of a Pyramid Example 2: Real-World Example: Lateral Area of a Pyramid Key Concept: Lateral and Surface Area of Cones Example 3: Surface Area of a Cone

Over Lesson 12–6 5-Minute Check 1 A.26,384.5 mm 2 B.28,274.3 mm 2 C.40,997.8 mm 2 D.41,002.3 mm 2 Find the lateral area of the figure.

Over Lesson 12–6 5-Minute Check 2 A.4.7 yd 2 B.4.9 yd 2 C.5.1 yd 2 D.5.3 yd 2 Find the surface area of the figure.

Over Lesson 12–6 5-Minute Check 3 A cm 2 B cm 2 C cm 2 D cm 2 Find the surface area of a cylinder with a diameter of 12 cm and a height of 29 cm.

Over Lesson 12–6 5-Minute Check 4 A.29.4 m B.30.7 m C.31.6 m D.32.3 m A cylinder silo has a lateral area of m 2. The silo has a diameter of 10 meters. What is the height?

Over Lesson 12–6 5-Minute Check 5 A.6,170 in 2 B.4,361 in 2 C.1,809 in 2 D.1,357 in 2 Edwin has two cylindrical ottomans. He wants to place slipcovers over them so that fabric would cover the top and sides, but not the bottom. How much fabric is needed to cover both ottomans?

Then/Now You have already found the surface areas of prisms and cylinders. (Lessons 12–5 and 12–6) Find lateral areas and surface areas of pyramids. Find lateral areas and surface areas of cones.

Vocabulary regular pyramid slant height

Concept A

Replace P with 8 4 and ℓ with 8.9 Example 1 Surface Area of a Pyramid Find the lateral and total surface area of the square pyramid. First find the lateral area. The lateral area of the pyramid is made up of four triangles. Write the formula. Simplify.

Example 1 Surface Area of a Pyramid Then find the surface area. The base of the pyramid is a square. S=L + BWrite the formula. = L + s 2 The area of a square is s 2. = Substitution =206.4 ft 2 Simplify. Answer: The lateral area of the square pyramid is square feet. The surface area of the square pyramid is square feet.

Example 1 A.16.5 m 2 B.33 m 2 C.42 m 2 D.75 m 2 Find the surface area of the square pyramid.

Example 2 Lateral Area of a Pyramid CANOPIES A canopy is in the shape of a square pyramid. If the length of each side is 3.4 meters and the slant height is 2 meters, how much canvas is needed for the canopy? Find the lateral area only, since there is no bottom to the canopy. Write the formula for lateral area. Replace P with 3.4 ● 4 and ℓ with 2.

Example 2 Lateral Area of a Pyramid L =13.6 m 2 Simplify. Answer: So, 13.6 square meters of canvas was used to cover the canopy.

Example 2 A.320 ft 2 B.224 ft 2 C.160 ft 2 D.80 ft 2 TENT A tent is in the shape of a square pyramid that is 8 feet on each side. The slant height is 10 feet. Find the lateral area of the tent.

Concept B

Example 3 Surface Area of a Cone Find the lateral and surface areas of the cone. Round to the nearest tenth. L=πrℓ Lateral area of a cone =π(3.5)(10) Replace r with 3.5 and ℓ with 10. ≈ ft 2 Simplify. Find the lateral area.

Example 3 Surface Area of a Cone Find the surface area. S=L + πr 2 Surface area of a cone ≈ π(3.5) 2 Replace L with 110 and r with 3.5. ≈ ft 2 Simplify. Answer:The lateral area is about square feet and the surface area is about square feet.

Example 3 CYP A cm 2 B cm 2 C cm 2 D cm 2 Find the surface area of the cone. Round to the nearest tenth.

End of the Lesson