SECTION 8.3SURFACE AREAS OF 3D SOLIDS
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I) REVIEW AREAS OF POLYGONS
Match each solid with the correct formula to find the area
Square
Triangle
Rectangle
Circle
Trapezoid
Now give the dimensions of each shape, find the area:
Square
Circle
Trapezoid
Triangle
Rectangle
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When finding the surface area of a 3D solid, get the areaof each side and then take the sum of all the sides
Note: we are getting the “AREA” of each side, NOT thelength of all the edges!!
Ex: Given the following prism, find the surface area:
SURFACE AREA OF A 3D SOLID:
First count the number of sides
There are 6 sides!!
Front
Back
Left
Right
Top
Bottom
Find the area of each side. You needthe shape and dimensions
Now get the sum:
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PRACTICE: FIND THE SURFACE AREA
Count the number of sides the prism has:
There are 5 sides
Front
Back
Left
Right
Bottom
Determine the shape of each side, find thedimensions and calculate the area
Triangle:
Triangle:
Rectangle:
Rectangle:
Rectangle:
To get the surface area, add all the areas ofeach side
Surface Area:
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PRACTICE: FIND THE SA OF THE FOLLOWING SOLID
First check that all the necessary lengths are given
For instance, we’re missing the length of this hypotenuse
Need the Pythagorean thm to calculate this length
Now get the SA by getting the sum of all five sides
Top
Bottom
Left
Right
Front
Surface Area:
The Four sides(Triangles)
Bottom
Surface Area
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EX: JIM WANTS TO PAINT THE EXTERIOR WALLS OF HIS HOUSE.CALCULATE THE SURFACE AREA THAT HE NEEDS TO PAINT:
Dimensions of his house:
There are 12 windows [2m x 0.5m]
There are 2 doors [2m x 2m]
Count the number of sides and theshape of each side
Note: He doesn’t paint the roof or thebottom of the house
Left/Right
Front/Back
These are justrectangles
These are pentagons
Rectangle & triangle on top
Surface Area
Now we subtractthe area of all the
windows and doors
The area of each window is 1m2
The area of each door is 4m2
The total area of all the windowsand doors is:
Now the total surface areathat needs to be painted is:
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