Post on 05-Jan-2016
Section 12.1Section 12.1
Areas and Volumes of PrismsAreas and Volumes of Prisms
PRISMS
What is a prism?What is a prism?
A A prismprism is a polyhedron with a is a polyhedron with a pair of congruent pair of congruent basesbases, that lie , that lie in parallel planes. in parallel planes.
The vertices of the bases are The vertices of the bases are joined to form the joined to form the lateral lateral facesfaces of a prism. of a prism.
Prisms are named according to Prisms are named according to the shapes of their bases.the shapes of their bases.
PARTS of a PRISMPARTS of a PRISM
BASE
FACE
HEIGHT
BASE
FACE
HEIGHT
CROSS SECTIONSCROSS SECTIONS
What is a What is a cross section??
Right vs. ObliqueRight vs. Oblique
If theIf the lateral edges of a prism lateral edges of a prism are perpendicular to its bases, are perpendicular to its bases, the prism is a the prism is a right prismright prism. .
If the lateral edges of a prism If the lateral edges of a prism are are notnot perpendicular to the perpendicular to the bases, the prism is an bases, the prism is an oblique oblique prismprism..
Right Prisms vs. Oblique Right Prisms vs. Oblique PrismsPrisms
1)1) Right PrismRight Prism
2)2) Oblique PrismOblique Prism
LATERAL AREALATERAL AREA
L.A. = L.A. = phph
p = perimeter of the basep = perimeter of the base
h = height of the prismh = height of the prism
TOTAL AREATOTAL AREA
The sum of the areas The sum of the areas of each face.of each face.
T.A. = L.A. + 2BT.A. = L.A. + 2B
VOLUME of a PRISMVOLUME of a PRISM
V = BhV = BhBB = area of the Base = area of the Base
hh = height of the prism = height of the prism
A right trapezoidal prism is A right trapezoidal prism is shown. Find the lateral area, shown. Find the lateral area,
total area, and volume.total area, and volume.
4 cm
10 cm
5 cm 5 cm
6 cm
12 cm
Height of prism
Height of trapezoidal base
4 cm
10 cm
5 cm 5 cm
6 cm
12 cm
LA = ph p = 12 + 6 + 5 + 5 = 28h = 10
LA = 28 ∙ 10 = 280
TA = LA + 2BTA = LA + 2( h(b½ 1 + b2))TA = 280+2( ∙4(12+6 ½))TA = 280+2(2(18 ))TA = 280+2(36)TA = 280+72TA = 352
V = BhV = ( h(b½ 1 + b2)) hV = ( ·4(12+6)) ½10V = (2(18)) 10V = (36) 10V = 360
A right triangular prism is A right triangular prism is shown. Find the lateral area shown. Find the lateral area
and total area since the and total area since the volume = 315.volume = 315.
h
7 6.54
10.5
h
7 6.54
10.5
V = Bh315 = Bh315 = ( bh)½ h315 = ( ·10.5·4)½ h315 = (21)h 15 = h
LA = ph p = 7+10.5+6.5=24h = 15LA = 24·15 LA = 360
TA = LA + 2BTA = LA + 2(½bh)TA = 360 + 2 (½·10.5·4)TA = 360 + 2 (21)
TA = 360 + 42TA = 402