CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-1 PRISMS.

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Presentation transcript:

CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-1 PRISMS

PRISM Prisms are 3-dimensional solids that have the following characteristics: 1.Bases 2.An altitude 3.Lateral faces 4.Lateral edges

BASES OF A PRISM Every prism has two bases that are congruent polygons lying on parallel planes. **Bases of a prism can be any figure from chapter 11 except for circles: Squares, rectangles, parallelograms, triangles, rhombuses, trapezoids, and regular polygons.

ALTITUDE OF A PRISM An altitude of a prism is a segment that joins the two base planes and is perpendicular to both. The length of the altitude of a prism is also known as the height of the prism (H).

LATERAL FACES A prism has multiple “faces” which include the bases of the prism. The lateral faces of a prism that are not its bases are called lateral faces. The lateral faces of an oblique prism are parallelogram. The lateral faces of a right prism are rectangles.

LATERAL EDGES Lateral edges of a prism occur where adjacent lateral faces meet. How you doin? What’s up?

OBLIQUE VS. RIGHT PRISM OBLIQUE PRISMRIGHT PRISM

PRISMS Right Pentagonal Prism BASES LATERAL FACE LATERAL EDGE ALTITUDE (H)

PRISMS Right Triangular Prism BASE LATERAL FACE LATERAL EDGE ALTITUDE (H) BASE

PRISMS Right Trapezoidal Prism BASE LATERAL FACE LATERAL EDGE ALTITUDE (H) BASE

THEOREM 12-1 The lateral area of a right prism equals the perimeter of a base times the height of the prism. L.A. = p H

LATERAL AREA In short, the lateral area of a right prism is the sum of the areas of the lateral faces. Remember, the lateral faces of a right prism are rectangles. Lateral AREA is measured in square units (units²).

TOTAL AREA Total area of a prism refers to the sum of the areas of all faces and, just like lateral area, is measured in square units. “All faces” of a prism include the lateral faces and bases. Total area of a prism is found by adding the lateral area to the area of both of the bases. T.A. = L.A. + 2B

THEOREM 12-2 The volume of a right prism equals the area of a base times the height of the prism. V = B H

VOLUME Volume is a 3-dimensional measure and is reported in cubic units (units³). The formula for volume includes a capital B which represents the area of the base.

AREA OF A BASE OF A PRISM “B” can be any of the following: 1.s²Square 2.bh Rectangle, parallelogram 3.½ bhTriangle 4.½ d 1 d 2 Rhombus 5.½ h (b 1 + b 2 )Trapezoid 6.½ apRegular polygon

CLASSWORK/HOMEWORK 12.1 ASSIGNMENT Classwork: Pg. 477, Classroom Exercises 2-10 even Homework: Pgs , Written Exercises 2-26 even