unit five lesson 6 surface area: prisms and pyramids

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


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.


There are 5 faces to this triangular prism.

Two ends are the same.

Three sides depend on the type of triangle:

Equilateral

Isosceles

Scalene


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


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.


There are 5 faces to this triangular pyramid.

One square bottom

Four triangular sides are the same.


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


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

unit five lesson 6 surface area: prisms and pyramids

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