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Section 12.2 Notes

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Prisms

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Prism and its Parts A prism is a three-dimensional figure, with two congruent faces called the bases, that lie in parallel planes. The other faces of a prism, called the lateral faces, are formed by connecting the corresponding vertices of the bases. In this book, the lateral faces of prisms are rectangles.

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A prism’s vertices are connected by segments called edges.

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Base Edges Lateral face Vertex

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The prism on the previous slide is called a triangular prism. Prisms are classified by the shape of their bases.

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Net Imagine cutting the triangular prism along some of its edges, then opening and unfolding it. The resulting plane figure is called a net.

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Net of triangular prism

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Surface Area of Prisms

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Surface Area The surface area is the area of the net for a three-dimensional figure. It is abbreviated SA.

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Lateral Area The lateral area is the area of the lateral faces (sides). It is abbreviated LA.

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Lateral Area of a Prism LA = ph, where p = the perimeter of the base and h = the height of the prism. The height of a prism is the length of a lateral edge.

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Surface Area of a Prism SA = LA + area of bases = ph + 2B

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Example 1 Find the SA of a triangular prism with an isosceles triangle as a base and a height of 6 cm. 13 cm 10 cm

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13 cm 10 cm h = 6 cm.

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Example 2 Find the surface area to the nearest tenth of pentgonal prism with a regular pentagon as a base and a height of 10 ft. 6 ft.

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a 36

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Example 3 Find SA of a hexagonal prism with a regular hexagon as a base with side length of 10 yds. and a height of 12 yds. 10 yds. h = 12 yds.

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10 yds. h = 12 yds. a 30

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Example 4 Find the surface area of a prism with regular hexagonal bases with an apothem of 6.9 cm, each base edge has a length of 8 cm, and the prism has a height of 10 cm.

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Example 5 Find the surface area of a right prism whose bases are equilateral triangles with side length of 4 cm. And the height of the prism is 10 cm. 4 cm h = 10 cm

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4 cm h = 10 cm a 60

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Cylinders

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Cylinder A cylinder is a figure in space whose bases are circles of the same size. The height of cylinder is the distance from the center of one base to the center of the other base. Base height

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Net of a Cylinder LA = Ch h

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Surface Area of Cylinders

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Surface Area of a Cylinder The surface area of a cylinder is the sum of the lateral area and the area of the bases.

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Surface Area Formula SA = 2πrh + 2πr 2, where r is the radius of the bases and h is the height of the cylinder.

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Example 6 Find the surface area of the cylinder. 2 cm. C = 20 cm. r = 10 cm.

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Example 7 10 cm 6 cm. Find the surface area of this right cylinder.

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Example 8 Find the surface area of a cylinder with a diameter of 10 cm. and a height of 5 cm.

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