Surface Area of Prisms and Cylinders

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Vocabulary• A net is a pattern you can fold to

form a three-dimensional figure.

This is a net for a triangular prism.

• The surface area of a three-dimensional figure is the sum of the areas of its surfaces.

• Find the area of each surface, and add all the areas together.

Example 1

26 cm

8 cm18 cm

Triangles

A = ½ bhA = ½ (26)(18)A = ½ (468)A = 234 cm2

2 Tri’s: 234 x 2 = 468 cm2

Left Rectangle

A = lwA = (18)(8)A = 144 cm2

Front and Back RectanglesA = lwA = (26)(8)A = 208 cm2

2 Rect’s: 208 x 2 = 416 cm2

Add up the areas to find surface area.

S.A. = 468 cm2 + 144 cm2 + 416 cm2

S.A. = 1,028 cm2

Surface Area of a Cube

• A cube has 6 congruent square faces.

• Find the area of one face, and multiply it by 6.

Example

7 in

A = s2

A = 72

A = 49 in2

S.A. = 49(6)

S.A. = 294 in2

Surface Area of a Rectangular Prism

• The surface area of a rectangular prism is the area of the six rectangles that cover it.

• To find the surface area, we don't have to figure out all six because we know that the top and bottom (length x width) are the same, the front and back (length x height) are the same, and the left and right sides (width x height) are the same.

• So, we can use the formula SA = 2(lh) + 2(lw) + 2(wh)

Surface Area of a Rectangular Prism

10 cm

7 cm

6 cm

SA = 2(lh) + 2(lw) + 2(wh)

SA = 2(6cm x 10cm) + 2(6cm x 7cm) + 2(7cm x 10cm)

SA = 2(60cm²) + 2(42cm²) + (70cm²)

SA = 120cm² + 84cm² + 140cm²

SA = 344cm²

Surface Area of a Cylinder• A cylinder consists of two circle bases

and one rectangular side.

• The length of the rectangle is equal to the circumference of the circle.

• Find the area of the circles and add it to the area of the rectangle.

Example5 m

16 m

Area of the circles

A = r2

A = 3.14(52)A = 3.14 (25)A = 78.5 m2

2 circles: 78.5 x 2 = 157 m2

Rectangle

The width of the rectangle is the height of the cylinder (16 m). The length of the rectangle is the circumference of the circle.

C = 2rC = 2(3.14)(5)C = 31.4 m

A = lwA = 31.4(16)A = 502.4 m2

Put the areas together:

S.A. = 157 m2 + 502.4 m2

S.A. = 659.4 m2

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