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Area and Volume of

Area and Volume of. Prism. 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.

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Area and Volume of

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  1. Area and Volume of Prism

  2. 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 The points where the edges intersected are called the vertices.

  3. Faces of A PRISM FACES

  4. Edges AND VERTICESof A PRISM

  5. PR I SM 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. PR I SM base Lateral face Lateral edge base

  7. Altitude of a prism 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. • T = L + 2B.

  10. Example #1: L = Ph =( 10 + 10 + 10+ 10)x2 = 80cm2 10 cm T = L + 2B = 16+2 x (10) = 180 cm2 10 cm V = Bh = 10 x 10 = 100 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. • 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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