Holt CA Course Surface Area AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C =  d–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Also covered: AF3.2 California Standards 1212

Holt CA Course Surface Area Vocabulary surface area net

Holt CA Course Surface Area 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 an arrangement of two-dimensional figures that can be folded to form a three-dimensional figure.

Holt CA Course Surface Area Additional Example 1: Finding the Surface Area of a Prism Find the surface area S of the prism. A. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.

Holt CA Course Surface Area Additional Example 1A Continued A: A = 5  2 = 10 B: A = 12  5 = 60 C: A = 12  2 = 24 D: A = 12  5 = 60 E: A = 12  2 = 24 F: A = 5  2 = 10 S = = 188 Add the areas of each face. The surface area is 188 in 2.

Holt CA Course Surface Area Additional Example 1: Finding the Surface Area of a Prism Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

Holt CA Course Surface Area Additional Example 1B Continued Front: 9  7 = 63 Top: 9  5 = 45 Side: 7  5 =  2 =  2 =  2 = 70 S = = 286 Add the areas of each face. The surface area is 286 cm 2.

Holt CA Course Surface Area Check It Out! Example 1 Find the surface area S of the prism. A. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face. 3 in. 11 in. 6 in. 11 in. 6 in. 3 in. A B C DE F

Holt CA Course Surface Area Check It Out! Example 1A Continued A: A = 6  3 = 18 B: A = 11  6 = 66 C: A = 11  3 = 33 D: A = 11  6 = 66 E: A = 11  3 = 33 F: A = 6  3 = 18 S = = 234 Add the areas of each face. The surface area is 234 in in. 6 in. 3 in. A B C DE F

Holt CA Course Surface Area Check It Out! Example 1 Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces. 6 cm 10 cm 8 cm top front side

Holt CA Course Surface Area Check It Out! Example 1B Continued Side: 10  8 = 80 Top: 10  6 = 60 Front: 8  6 =  2 =  2 =  2 = 96 S = = 376 Add the areas of each face. The surface area is 376 cm 2. 6 cm 10 cm 8 cm top front side

Holt CA Course Surface Area The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net.

Holt CA Course Surface Area Additional Example 2: Finding the Surface Area of a Pyramid Find the surface area S of the pyramid. S = area of square + 4  (area of triangular face) S =  28 S = Substitute. S = s  ( bh) 1 2 __ S =  (  7  8) 1 2 __ S = 161 The surface area is 161 ft 2.

Holt CA Course Surface Area Check It Out! Example 2 Find the surface area S of the pyramid. S = area of square + 4  (area of triangular face) S =  25 S = Substitute. S = s  ( bh) 1 2 __ S =  (  5  10) 1 2 __ S = 125 The surface area is 125 ft 2. 5 ft 10 ft 5 ft

Holt CA Course Surface Area 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

Holt CA Course Surface Area Additional Example 3: Finding the Surface Area of a Cylinder Find the surface area S of the cylinder. Write your answer in terms of . S = area of curved surface + (2  area of each base) Substitute 7 for h and 4 for r. S = (h  2r) + (2  r 2 ) S = (7  2  4) + (2    4 2 ) ft S = (7  2  4)+ (2    16) Simplify the power.

Holt CA Course Surface Area Additional Example 3 Continued Find the surface area S of the cylinder. Write in terms of . S = ( ) The surface area is about 88 ft 2. Multiply. S = 88 S = 56 + 32 Use the Distributive Property.

Holt CA Course Surface Area Check It Out! Example 3 Find the surface area S of the cylinder. Write your answer in terms of . S = area of lateral surface + (2  area of each base) Substitute 9 for h and 6 for r. S = (h  2r) + (2  r 2 ) S = (9  2  6) + (2    6 2 ) 6 ft 9 ft S = (9  2  6) + (2    36) Simplify the power.

Holt CA Course Surface Area Check It Out! Example 3 Continued Find the surface area S of the cylinder. Write your answer in terms of . S = ( ) S = 180 The surface area is about 180ft 2. Multiply. S = 108 + 72 Use the Distributive Property.