10.9 Surface Area 6.4.5 – I can find the surface areas of prisms, pyramids, and cylinders.

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10.9 Surface Area 6.4.5 – I can find the surface areas of prisms, pyramids, and cylinders

Warm Up Identify the figure described. 1. two parallel congruent faces, with the other faces being parallelograms 2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles prism pyramid

The surface area of a three- dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is the pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure.

What is the surface area of this prism?

Find the surface area S of the prism. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face. The surface area is 188 in 2.

Find the surface area S of each prism.

Front: 9  7 = 63 Top: 9  5 = 45 Side: 7  5 = 35 63  2 = 126 45  2 = 90 35  2 = 70 S = 126 + 90 + 70 = 286Add the areas of each face. The surface area is 286 cm 2.

3 in. 11 in. 6 in. The surface area is 234 in 2.

6 cm 10 cm 8 cm The surface area is 376 cm 2.

S = area of square + 4  (area of triangular face) ‏ The surface area is 161 ft 2.

S = area of square + 4  (area of triangular face) ‏ The surface area is 125 ft 2. 5 ft 10 ft 5 ft

The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface. To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base. Helpful Hint

Surface Area of a Cylinder A cylinder has a total of three surfaces: a top, bottom, and middle. The top and bottom, which are circles, are easy to visualize. The area of a circle is πr 2

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = area of curved surface + 2  (area of each base) ‏ The surface area is about 276.32 ft 2. Video

Find the surface area of each figure. Use 3.14 for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. 214 ft 2 188.4 ft 2 208 ft 2

2. Find the surface area of a cylinder with radius 5 ft and height 8 ft. Use 3.14 for  A. 576.8 ft 2 B. 408.2 ft 2 C. 376.2 ft 2 D. 251.2 ft 2

3. Find the surface area of the figure shown. A. 162 ft 2 B. 152 ft 2 C. 142 ft 2 D. 132 ft 2

Square Pyramid 5.6 ft 4.8 ft

Triangular Prism 6 in 3 in

Cylinder 24 in 12 in 4 in

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