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Area and Volume of

Area and Volume of. Prism. DEFINITION: PRISMS. INTRODUCTION:

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Area and Volume of

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  1. Area and Volume of Prism

  2. DEFINITION: PRISMS INTRODUCTION: A polyhedron is a geometric figure made up of a finite number of polygons that are joined by pairs along their sides and that enclose a finite portion of space. The polygons that make up a polyhedron are called the faces, the common sides are called the edges intersect are called the vertices.

  3. Faces of A PRISM FACES

  4. Edges AND VERTICES A of PRISM

  5. PRISM • A polyhedron is a PRISM if and only if has two congruent faces that are contained in parallel planes, and its other faces are parallelograms. • The two congruent faces are the bases ; the other faces are the lateral faces. Lateral faces intersect in the lateral edges, all of which are parallel and congruent.

  6. base Lateral edge Lateral face base

  7. A segment is an altitude of a prism if and only if it is perpendicular to the planes of both bases of the prism. The length of the altitude of a prism is called the height of the prism. In a right prism, the height is the same as the length of any lateral edge.

  8. Area of A PRISM THEOREM 12.1 The lateral area L of a right prism equals the perimeter of a base P times the height h of the prism or L = Ph.

  9. Theorem 12.2 The total area T of a right prism is the sum of the lateral area L and the area of the two bases 2B or T = L + 2B.

  10. Example #1: L = Ph =( 2 + 2 + 2 + 2) x 2 = 16 cm2 10 cm T = L + 2B = 16 + 2 x (2 x 2) = 24 cm2 10 cm V = Bh = (2 x 2 ) x 2 = 8 cm3 10 cm

  11. Volume of A PRISM The Volume is the amount of space occupied by the figure.

  12. THEOREM 12.3 The volume V of a prism equals the area of a base B times the height h of a prism or V = Bh. Corollary : The volume of a cube with edge e is the cube of e, or V = e3.

  13. Using the Pythagorean Theorem, the third side of the base is 10 cm. The area of the base B is 1/2 h x b = 1/2 (6) (8) = 24 m2 Example #2: L = Ph =( 6 + 8 + 10) x (12) = 288 m2 6 m 8 m T = L + 2B = 288 + 2 (24) = 336 m2 V = Bh = 24 x 12 = 288 m3 12 m

  14. PREPARED BY: MIRIAM C. TORREJA III-B MATH

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