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Mrs. Bothers
East Cobb Middle School(Adapted from Mr. Tauke’s PPT)
Application: How much cardboard does it take to make a cardboard box?
The manufacturers have to know this in order to make the boxes.
When wrapping gifts, you are covering the outside of the
box. This is another example of surface area of a rectangular prism.
Looking at the net, you see that TO FIND THE SURFACE AREA OF A RECTANGULAR PRISM, YOU NEED TO FIND THE AREA OF ALL 6 FACES.
Let’s explore this idea…
Do you see the RED (front) face?
4 in.
7 in.
10 in.
What are the dimensions of this rectangle?
10 in.
4 in.
Do you see another face that is just like the RED (front) face?
Where is it located?
4 in.
7 in.
10 in.
Keep an eye on the next screen!
Yes, it’s on the back.
10 in.
4 in.
10 in.
4 in.
FRONT BACK
Now there are 2 rectangles
40 in2
40 in2
that each have an area of 40 sq. in.
4 in.
7 in.
10 in.
Do you see the BLUE (side) face?What are the dimensions of this rectangle?
4 in.
7 in.
Do you see another face that is just like the BLUE face?
Where is it located?
4 in.
7 in.
10 in.
Yes, it’s on the left side.
4 in.
7 in.
7 in.
4 in.
SIDE 1 SIDE 2
Now there are 2 rectanglesthat each have an area of 28 sq. in.
28 in2
28 in2
4 in.
7 in.
10 in.
Do you see the GREEN
(top) face?
What are the dimensions of this rectangle?
10 in.
7 in.
Do you see another face that is just like the GREEN face?Where is it
located?
4 in.
7 in.
10 in.
Yes, it’s on the bottom.
10 in.
7 in.
10 in.
7 in.
BOTTOM TOP
Now there are 2 rectanglesthat each have an area of 70 sq. in.
70 in2
70 in2
Now we just need to add all the areas of the sides together.
+ +
++ 70 in2
28 in2
40 in2
40 in2
28 in2
70 in2
The total Surface Area for this
rectangular prism is40 + 40 + 28 + 28 +
70 + 70 =
276 in2
4 in.
7 in.
10 in.
2(lw) + 2(wh) + 2(lh)
2(40) + 2(28) + 2(70)
80 + 56 + 140
276 in2
Use the formula:2(lw) + 2(wh) + 2(lh)
2(3•4) + 2(4•12) + 2(3•12)
2(12) + 2(48) + 2(36)
24 + 96 + 72
192 cm2
What is special about a cube?
It has 6 square faces! Using the example to the left, what is the area of 1 face?
5 • 5 = 25 ft2
Since there are 6 equal faces, what is the surface area?
6 • 25 = 150 ft2
So, for SA of a cube, find the area of one face and then multiply by 6. What do you think the formula is?
Yea, good job!! SA Cube = 6s2
(s = length of one side)
What is the area of this cube, if its height is 8 in.?
6 • 82
6 • 64384 in2
SA Rect. Prism = 2(lw) + 2(wh) + 2(lh) SA Cube = 6s2
1) What is the surface area of a pizza box that has a length of 10 in, a width of 12 in, and a height of 2 in?
2) How much wrapping paper is needed to cover a box that is 7 cm long, 8 cm wide, and 3 cm tall?
3) What is the surface area of a Rubik’s Cube that is 3 inches tall?
4) Which has more surface area, a cube that is 10 in wide, or a rectangular prism that is 12 in wide, 10 in long, and 8 in tall?1) 328 in2 2) 202 cm2 3) 54 in2 4) cube = 600in2, rect.
prism = 592in2
Now, begin your homework. Be sure to
use the correct formulas and SHOW ALL YOUR WORK!
