unit five lesson 6 surface area: prisms and pyramids
TRANSCRIPT
Unit Five Lesson 6
Surface Area: Prisms and Pyramids
3 easy steps to calculate the Surface Area of a solid figure
1. Determine the number of surfaces and
the shape of the surfaces of the solid
2. Apply the relevant formula for the area of
each surface
3. Sum the areas of each surface
Surface Area – Basic concept
Determine the number and shape
of the surfaces
that make up the solid.
It might be easier to think of the net of the solid.
square rectanglerectangle square
rectangle
rectangle
4 rectangular faces and 2 square
faces
When you’ve done all that find the area of each face and then find the total of the areas.
Square prism
18 cm
2410
904252
1854552
cmA
A
A
Two square faces
Find the surface area of this figure with square base 5 cm and height 18 cm
5 cm
Four rectangular faces
Rectangular prism
5 cm15 cm
20 cm
155A
155A
205A
205A2015A 2015A
2950
30021002752
2015220521552
cmA
A
A
Now sum
these areas
Find the surface area of this figure with length 10 cm, width 15 cm and height 12 cm.
The surface area of a prism is the entire area of the outside of the object.
To calculate surface area, find the area of each side and add them together.
There are 6 faces to this rectangular prism.
Front and back are the same
Top and Bottom are the same
Two ends are the same.
To find the surface area, add the areas together.
Top and Bottom
A = bh
A = (90)(130)
A = 11700 cm2
Ends
A = bh
A = (90)(50)
A = 4500 cm2
Front and back
A = bh
A = (130)(50)
A = 6500 cm2
Total Surface Area = 2(top and Bottom) + 2(Ends) + 2(Front and Back)
= 2(11700) + 2(4500) + 2(6500)
= 45 400 cm2
To find the surface area, add the areas together.
To find the surface area, add the areas together.
Top and Bottom
A = bh
A = (4)(10)
A = 40 m2
Ends
A = bh
A = (2)(4)
A = 8 m2
Front and back
A = bh
A = (2)(10)
A = 20 m2
Total Surface Area = 2(top and Bottom) + 2(Ends) + 2(Front and Back)
= 2(40) + 2(8) + 2(20)
= 136 m2
Triangular Prism
12 cm
20 cm10 cm
2010A 2010A 2012A
2736
24040096
2012201028122
12
cmA
A
A
Hence, total surface area
8122
1A
Find the surface area of this figure with dimensions as marked.
12 cm
10 cm
6
8
height 8 cm
Determine the number of faces and the shape of
each face
Apply the area
formulae for each face
Sum the areas to give
the total surface area
Square Pyramid
10 cm
P
Q
13102
1A 1310
2
1A 1310
2
1A 1310
2
1A 1010A
Find the surface area of this figure with square base 10 cm and height 12 cm.
4 triangular faces with the same
dimensions and 1 square face
We need to find the height of each triangular
face. 10
13
T
P height 13 cm.
12
2360
100260
101013102
14
cmA
A
A
Hence, total surface area
The surface area of a triangular prism is the entire area of the outside of the object.
To calculate surface area, find the area of each side and add them together.
There are 5 faces to this triangular prism.
Two ends are the same.
Three sides depend on the type of triangle:
Equilateral
Isosceles
Scalene
To find the surface area, add the areas together.
Bottom
A = bh
A = (1.3)(2.1)
A = 2.73 m2
Ends
A = bh 2
A = (1.3)(0.5) 2
A = 0.325 m2
Front
A = bh
A = (2.1)(0.5)
A = 1.05 m2
Total Surface Area = Bottom + 2(Ends) + Front + Back
= 2.73 + 2(0.325) + 1.05 + 2.52
= 6.95 m2
Back
A = bh
A = (2.1)(1.2)
A = 2.52 m2
To find the surface area, add the areas together.
To find the surface area, add the areas together.
Sides
A = bh
A = (1)(3)
A = 3 m2
Ends
A = bh 2
A = (1)(0.866) 2
A = 0.433 m2
Total Surface Area = 2(Ends) + 3(sides)
= 2(0.433) + 3(3)
= 9.866 m2
a2 = c2 - b2
a2 = (1)2 - (0.5)2
a2 = 1 - 0.25
a2 = 0.75
a = 0.866
Height = .866
The surface area of a pyramid is the entire area of the outside of the object.
To calculate surface area, find the area of each side and add them together.
There are 5 faces to this triangular pyramid.
One square bottom
Four triangular sides are the same.
To find the surface area, add the areas together.
Bottom
A = s2
A = (4)(4)
A = 16 cm2
sides
A = bh 2
A = (4)(3) 2
A = 6 cm2
Total Surface Area = Bottom + 4(sides)
= 16 + 4(6)
= 40 cm2
To find the surface area, add the areas together.
To find the surface area, add the areas together.
Bottom
A = s2
A = (5)(5)
A = 25 cm2
sides
A = bh 2
A = (5)(6) 2
A = 15 cm2
Total Surface Area = Bottom + 4(sides)
= 25 + 4(15)
= 85 cm2
Practice page 178 and 179
Odd #1 - 13