Finding Surface Area of Prisms

Rectangular Prisms and Cubes

Picture the net of each figure.

Surface area is the total area of each side or face of a figure.

How many sides does a cube have?

How many sides does a rectangular prism have?

http://www.brainingcamp.com/resources/math/surface-area/surface-area-lesson.php

So, the surface area is 1,674 m2.

http://www.google.com/imgres?imgurl=http://mathforum.org/alejandre/escot/cube.net.gif&imgrefurl=http://mathforum.org/alejandre/escot/cube.prism.html&h=559&w=433&sz=5&tbnid=TI6Auu0xWZl5nM:&tbnh=256&tbnw=198&prev=/images%3Fq%3Dnet%2Bof%2Ba%2Brectangular%2Bprism&usg=__t5lGBTF-LzCpO1MWblY2CqUEKj8=&ei=kW2BS4-_M8WVtgfz--WUBw&sa=X&oi=image_result&resnum=3&ct=image&ved=0CAYQ9QEwAg

Example 1Find the surface area for this rectangular prism.

                         

SA = 2 • Top + 2 • Front + 2 • LeftSA = 2lw + 2lh + 2whSA = 2 • 4 • 3 + 2 • 4 • 5 + 2 • 3 • 5SA = 24 + 40 + 30SA = 94 cm2

 

Example 2Find the surface area for this rectangular prism.

                             

     

SA = 2 • Top + 2 • Front + 2 • LeftSA = 2lw + 2lh + 2whSA = 2 • 6 • 3 + 2 • 6 • 3 + 2 • 3 • 3SA = 36 + 36 + 18SA = 90 cm2

 

• How is finding surface area similar to finding area of a polygon?

• How can knowing a figure’s net help you find surface area?

• Do you have to know the formula to find surface area?

Finding Surface Area of Prisms

Triangular Prisms

Picture the net of each figure.

http://www.brainingcamp.com/resources/math/surface-area/surface-area-lesson.php

SA= 2B +bh+bh+bh

SA = 2(bh÷2) + bh+bh+bh

So, the total surface area of the given solid is 360 cm2.

The surface area of the prism is 210 cm2.

Finding Surface Area of Cylinders

Cylinders

Picture the net of each figure.

http://www.brainingcamp.com/resources/math/surface-area/surface-area-lesson.php

  SA = 2B + bh+bh+bh

SA = 2(bh ÷ 2) + bh+bh+bh

                      

So, the total surface area is approximately 125.6.

So, the surface area of the cylinder is about 180.9 cm2.

Finding Surface Area of Pyramids

Square Pyramids and Triangular Pyramids

Picture the net of each figure.

http://www.brainingcamp.com/resources/math/surface-area/surface-area-lesson.php

The surface area of a pyramid is the sum of the area of the base plus the areas of the

lateral faces.This simply means the sum of the areas of all

faces.

                                  

                                         

The surface area, S, of a regular pyramid can be found using

the formula                                   .B = area of base, p = perimeter of base, s = slant height.

 

                          

                                                                                        

A net is a two-dimensional figure

that can be cut out and folded up to

make a three-dimensional solid.

  SA = 2B + Ph SA = 2(1/2ab) + (b + c + d)hSA = ab + (b + c + d)h

                      Square Pyramid:

SA= 4(bh÷2) + B

• To Find the surface area of a Triangular Pyramid:

• SA = 4B or 4(bh÷2)

4.2 cm

5 cm

5 cm SA = 42 cm ²

• What to do for a rectangular pyramid:

• SA = B + Area of the 4 triangles (the triangles will be different because the base is not a square. Two triangles will be equal and the other two will be equal.

1.5

cm

6 cm

2 c

m

SA = (bh) + 2(bh÷2) + 2(bh÷2)

SA = (6x2) + 2(6x1.5 ÷2) + 2(2x1.5 ÷2)

SA = 12 + 2(4.5) + 2(1.5)

SA = 12 + 9 + 3

SA = 24 cm²

5 cm 8 cm

8 cm

10

cm

11.5 cm

12 cm

14 cm

22 cm

11 c

m

13 cm

9 cm

3 c

m

5 cm

7 cm

4 cm