1. Surface Area of Prisms

2. Vocabulary
Surface Area: the sum of the areas of all the faces of a 3D figure
Measured in square units (ex: ft2, in2, m2, 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 base

3. Examples of Prisms
Hexagonal Cube Rectangular Prism Triangular Prism Prism

4. Cube – special because all six faces are identical
Find the area of one of the faces
Area of square = s2 or bh
3*3 = 9 yd2
Since all six faces are exactly the same, multiply the area of one face by 6
9 yd2 * 6
Surface area = 54 yd2
3 yd
3 yd
3 yd

5. Practice Cube

6. 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 cm2
Find the area of one of the rectangles
Area of rectangle = bh = 13*7 = 91cm2
There are 2 hexagons so multiply that area by 2. There are 6 rectangles so multiply that area by 6.
Hexagons: 2 * 546 = 1092 cm2
Rectangles: 6 * 91 = 546 cm2
Add the areas together: = 1638 cm2
7 cm
14 cm
13 cm

7. Practice Hexagonal Prism

8. 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 sizes

9. 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 area

10. Scalene Triangular Prism
Find area of triangular base
Area of triangle = ½ bh = ½ *8*9 = 36cm2
Find area of pink rectangle (bottom side) = bh = 8*5 = 40cm2
Find area of purple rectangle (left side) = bh = 9*5 = 45cm2
Find area of green rectangle (top side) = bh = 10 * 5 = 50cm2
There are two triangular bases so multiply that area by 2
36cm2*2 = 72cm2
Add all four areas together to get total surface area
72cm2 + 40cm2 + 45cm2 + 50cm2 = 207cm2

11. Practice Triangular Prisms

12. Rectangular Prism – all sides rectangles
3 pairs of congruent faces
Top/bottom
Front/back
Sides (left/right)
General Formula for Surface Area
2lw + 2wh + 2lh = SA
Those are “L”s not “1”s
ONLY APPLIES TO RECTANGULAR PRISMS

13. Rectangular Prism Example
L = 14cm
H = 8 cm
W = 7 cm
Formula: 2lw + 2wh + 2lh
(2*14*7) + (2*7*8) + (2*14*8)
532 cm2
7 cm
8 cm
14 cm

14. Rectangular Prism Practice