Areas and Volumes of Prisms

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Presentation transcript:

Areas and Volumes of Prisms Section 12.1 Areas and Volumes of Prisms

PRISMS

What is a prism? A prism is a polyhedron with a pair of congruent bases, that lie in parallel planes. The vertices of the bases are joined to form the lateral faces of a prism. Prisms are named according to the shapes of their bases.

PARTS of a PRISM FACE BASE HEIGHT FACE BASE HEIGHT

CROSS SECTIONS What is a cross section?

Right vs. Oblique If the lateral edges of a prism are perpendicular to its bases, the prism is a right prism. If the lateral edges of a prism are not perpendicular to the bases, the prism is an oblique prism.

Right Prisms vs. Oblique Prisms

L.A. = ph LATERAL AREA p = perimeter of the base h = height of the prism

TOTAL AREA The sum of the areas of each face. T.A. = L.A. + 2B

VOLUME of a PRISM V = Bh B = area of the Base h = height of the prism

A right trapezoidal prism is shown A right trapezoidal prism is shown. Find the lateral area, total area, and volume. Height of trapezoidal base Height of prism

LA = ph TA = LA + 2B p = 12 + 6 + 5 + 5 = 28 h = 10 LA = 28 ∙ 10 = 280 TA = LA + 2(½h(b1 + b2)) h = 10 TA = 280+2(½∙4(12+6 )) LA = 28 ∙ 10 = 280 TA = 280+2(2(18 )) TA = 280+2(36) TA = 280+72 TA = 352 V = Bh V = (½h(b1 + b2)) h V = (½·4(12+6)) 10 V = (2(18)) 10 V = (36) 10 V = 360

A right triangular prism is shown A right triangular prism is shown. Find the lateral area and total area since the volume = 315.

V = Bh TA = LA + 2B 315 = Bh 315 = (½bh)h 315 = (½·10.5·4)h TA = LA + 2(½bh) 315 = (½bh)h TA = 360 + 2 (½·10.5·4) 315 = (½·10.5·4)h TA = 360 + 2 (21) 315 = (21)h TA = 360 + 42 15 = h TA = 402 LA = ph p = 7+10.5+6.5=24 h = 15 LA = 24·15 LA = 360