Vocabulary Surface Area the sum of the areas of all the faces of a 3D figure Measured in square units ex ft 2 in 2 m 2 etc Faces sides of a figure Prism 3D shape with two congruent equal bases and parallelogram sides ID: 496533
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Slide1
Surface Area of PrismsSlide2
Vocabulary
Surface Area:
the sum of the areas of all the faces of a 3D figure
Measured in square units (ex: ft
2
, in
2
, m
2
,
etc
)
Faces:
sides of a figure
Prism:
3D shape with two congruent (equal) bases and parallelogram sides
Note:
the figure does not have to be sitting on its baseSlide3
Examples of Prisms
Hexagonal Cube Rectangular Prism Triangular Prism PrismSlide4
Cube
– special because all six faces are identical
Find the area of one of the faces
Area of square = s
2
or bh3*3 = 9 yd2Since all six faces are exactly the same, multiply the area of one face by 6
9 yd2 * 6Surface area = 54 yd2
3
yd
3
yd
3
ydSlide5
Practice Cube
6 in
6 in
6 inSlide6
Rectangular Prism
– all sides rectangles
3 pairs of congruent faces
Top/bottom
Front/back
Sides (left/right)
General Formula for Surface Area2lw + 2wh + 2lh
= SAThose are “L”s not “1”sONLY APPLIES TO RECTANGULAR PRISMSSlide7
Rectangular Prism Example
L = 14cm
H = 8 cm
W = 7 cm
Formula:
2lw +
2wh + 2lh (2*14*7) + (2*7*8) +
(2*14*8)196 + 112 + 224532 cm2
8 cm
14 cm
7 cmSlide8
Rectangular Prism Practice
15 in
3 in
6 inSlide9
Hexagonal Prism
– 2 hexagon bases and 6 identical rectangular sides
Find the area of one of the hexagons
Area of hexagon = 3bh = 3*14*13 = 546 cm
2
Find the area of one of the rectangles
Area of rectangle = bh = 13*7 = 91cm2There are 2 hexagons so multiply that area by 2. There are 6 rectangles so multiply that area by 6.
Hexagons: 2 * 546 = 1092 cm2Rectangles: 6 * 91 = 546 cm2Add the areas together:
1092 + 546 = 1638 cm2
7 cm
14 cm
13 cmSlide10
Practice Hexagonal Prism
12 cm
4
cm
2
cmSlide11
Triangular Prism
– 2 triangle bases and 3 rectangular sides*
If base is equilateral triangle, then all three rectangles will be the congruent
If base is isosceles or scalene triangle, then rectangles will be different sizesSlide12
Equilateral Triangular Prism
– all rectangles congruent
Find the area of one triangular base
Find the area of one rectangular side
There are 2 triangular bases so multiply that area by 2. There are 3 rectangular sides so multiply that area by 3.
Add the areas together to get the surface areaSlide13
Scalene Triangular Prism
Find area of triangular base
Area of triangle = ½
bh
= ½ *8*9 = 36cm
2
Find area of pink rectangle (bottom side) =
bh = 8*5 = 40cm2Find area of purple rectangle (left side) = bh = 9*5 = 45cm
2Find area of green rectangle (top side) = bh = 10 * 5 = 50cm2There are two triangular bases so multiply that area by 2
36cm
2
*2 = 72cm
2
Add all four areas together to get total surface area
72cm
2
+
40cm
2
+
45cm
2
+
50cm
2
=
207cm
2Slide14
Practice Triangular Prisms