Surface Area of Rectangular Prisms and Cubes

Please use your book (pages 423-427) to write down the work for this lesson. Today we will focus on cubes and rectangular prisms. Tomorrow we will do the triangular prisms. Make sure you show your work in your textbook. I will be checking the pages tomorrow. Have a great day!

Lesson 7-6

Find Surface Area of Prisms

There are 6 squares, so make sure you find the area of one square. Then you can multiply that by the 6 sides.

​

​How can you solve this?

Check your work.

This should be in your book...

Each square has a side length of 9 inches, so each square has an area of 81 sq in. If there are 6 squares,

6 x 81 = 486 inches squared

15 x 30 = 450 inches squared

​She needs 36 square inches more!

NO!

Kelly wants to cover a shoebox with decorative paper without overlapping the paper. How much paper will she need to cover the box?

​​Page 424 Ex. 1

​Open the box and use the net.

Notice, opposite rectangles are going to have the same area. Once you find the area of all 6, add them together.

One way...

Use the surface area formula.

SA = 2(lw) + 2(wh) + 2 (lh)

Do 2 times each rectangular face, then add them together.

Another way...

Use the net and formula to find the surface area of the prism.

SA=2(lw)+2(wh)+2(lh)

Try It!

Why are lw, wh, and lh each multiplied by 2 in the formula?

Because there are 6 rectangles, 2 of each.

(Opposite side are equivalent.)

Convince Me!

Assign a length, width and height (they can be interchangible).

If l = 4, w = 2, h = 3 then

SA = 2(4*2) + 2(2*3) + 2(4*3) so

2(8) + 2(6) + 2(12) = 16 + 12 + 24

SA = 52 cm²

SA=2(lw)+2(wh)+2(lh)

Check your work...

​You know that one side of a cube is a square, so if both sides of the square are 0.5m, then you would multiply 0.5 x 0.5 to get 0.25 meters squared. There are 6 sides on a cube, so multiply the area of one square by 6.

​​Ex. 2 - SA of a cube

0.25 x 6 = 1.5 m²

Answer:

Find the surface area of the cube. Show your work on page 425 part a.

​

Try It!

You can use the formula for a cube which is:

SA = 6s²

​

SA = 6(4.2)²

4.2 x 4.2 = 17.64

17.64 x 6 = 105.84 cm²

​

Check your work!

Turn to page 426 in your book. Please do # 5 and 6.

Then go to page 427 and do #8, 10, 11, 13, 14, 16, & 17. Show all of your work, I will be checking it tomorrow!

​

​Time to Practice!