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1.3 Skill Builder

Surface Areas of Rectangular Pris ms- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - --- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The surface area of a rectangular prism is the sum of the areas of its 6 rectangular faces.

Look for matching faces with the same areas.

The matching faces in each

pair have the same area.

We find the area of one

face and multiply by 2.

10 cm

For each rectangular face, area equals its length times its width.

Matching Faces Diagram Corresponding Area (cm2)

B kac .,

-^' 6cm 2(10x6)=120

6 cm . ,Front

,10 cm

10 cm

10 cm

8cm

To}

10cm

}8cm

2(10x8)160

Bottom

8cm /8cm

RighLeft. side.

6 cm side6 cm

2(8x6)96

Total376

The surface area is 376 cm2.

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------

?termine the surface area of each rectangular prism.

Matching Diagram Corresponding

Faces Area (cm2)

Front

B k

cm

_ cm_

Z(

X -^ - -ac

Top

Bottom

-CM

_ cm2(- X

) = _

Right_cm

X2(Left

El - cm

-

Total

2 cm

5 cm

The surface area is

cm2.


Faces Area (cm2)

Front

Back-CM 2(_ x

cm

Top CM 2X

Bottom

cm

Right

Left_ cm 2(

x

cm

Total

I

12 cm

The surface area is

cm2.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

23

Example 2a Composite Object

Finding the Surface Area o

I

Find the surface area of this composite object.

Solution

Surface area of

Surface area of

Surface area of

composite object

smaller prism

larger prism

Surface area of smaller prism


Faces Area (m2)

Front

Back6 m

TH3m 4(6X3)72

Right

Left

Top6 m

2(6X6)=72

Bottom q 6m

Total144

The surface area is 144 m2.

Area of overlap

Diagram Corresponding

Area (m2)

6m

=3m6x3=18

2(Area of overlap)

SA means surface area;

Surface area of larger prism


FacesArea (m2)

Front

Back12 m

4(12 x 6) = 288

Top6 m

Bottom

Right6 m

2(6 x 6) = 72

Leftq 6m

Total360

The surface area is 360 m2.

The area of overlap is 18 m2.

SA of composite object = 144 + 360 - 2(18) = 468

The surface area of the composite object is 468 m2.

26

Peck---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

. The diagram shows the surface areas of the two prisms that make up a composite object.

SA = 40 cm2

SA=70cm2

1 cm

a) What is the area of the overlap?

The overlap is a

-cm by

-cm rectangle.

Area of overlap =

cm x

cm

cm2

b) What is the surface area of the composite object?

SA composite object = SA smaller prism + SA larger prism - 2(Area of overlap)

cm2 +

cm2 - 2(

) cm2

cm2

. Find the surface area of this composite object.

6 cm

Front

A cube has

congruent faces.

27

3. Find the surface area of this composite object.

Front

Surface area of larger prismSurface area of smaller prism

Matching

Faces


Area (m2)

Front

Back2(^x `)=

Top

Bottom

Right

Left

Total

The surface area is m2.

Area of overlap

Diagram Corresponding Area (m2)

x

=

The area of overlap is

m2.

Surface area of composite object

SA composite object =

+

_

+

- 2(--_)

The surface area of the composite object is

m2.

The surface area is m2.

Matching

Faces


Area (m2)

Front

Back2(_xj=

Top

Bottom

Right

Left

Total

t. Find the surface area of this composite object.

30 cm

rface area of cubeFront

latching Faces Diagram Corresponding Area (cm2)

:ront / Backcm

op / Bottom 6(

x

tight / LeftCM

rotas

rface area of rectangular prism

The surface area is

cm2.

latching Faces Diagram Corresponding Area (cm2)

:ront / Back2(

x

bp / Bottom

tight / Left

rota IThe surface area is cm2.

ea of overlap

)iagram Corresponding Area (cm2)

x


irface area of composite object

composite object =

_

+

-

ie surface area of the composite object is

cmZ.

cm2.

11

0 . Surface Areas of Other Composite Objects

1 Find the surface areas of composite objects made from right prisms and

right cylinders.

Example I Finding the Surface Area of a Composite Object Made

from a Rectangular Prism and a Triangular Prism

Solution

10 cm

8 cm

------------------------------------------------------------------------------------------------------------------------------------------------------------------

--------------

10 cm

6 cm---- --------

Find the surface area

of this composite object.

The shaded area is

the area of overlap.

Surface area of Surface area of 2(Area of overlap)

composite object

rectangular prism

triangular prism

Surface area of rectangular prism Surface area of triangular prism

4 cm

Total248


Area of overlap

Diagram Corresponding Area (cm2)

6cm

4 cm

6X4=24

MatchingFaces


Area (cm2)MatchingFaces

2(6 x 10)

= 120

TriangularFront

Back6 cm

10 cm

Top

Bottom

10 cm

2(10 x 4)

= 804 cm

Right

Left2(6 x 4)= 48

6 cm

Rectangular

Diagram

6 cm

n8 cm

10 cm

6 cm

4 cm

4 cm

8 cm

Total


The area of overlap is 24 cm2.

Surface area of composite object = 248 + 144 - 2(24) = 344

The surface area of the composite object is 344 cm2.

36

Corresponding

Area (cm2)

2(ZX6x8)

= 48

10x4=40

6 x 4 = 24

8x4=32

4 cm

Peck---------------------------------------------------------------------------------------------------------------------------

The diagram shows the surface area of the

two prisms that make up a composite object.


The overlap is a

-cm by

-cm rectangle.

Area of overlap =

cm x

cm =

cmz


Surface area of composite object = Surface area of 2 prisms - 2(Area of overlap)


Find the surface area of this composite object.

4 cm

3 cm

cm3

Surface area of triangular prism


TriangularcmL 2L x

x

cm

.

cmx

=

cm

Rectangular -cm x

=

CM

cm

cmx

=

Total

The surface area is

cmz.

37

Surface area of cube


Front

Back

Top_ cm

6(_X

Bottom-CM

Right

Left

Total

Area of overlap


Area (cm2)

cm

CM

X


cm2.

The surface area is

cm2.

Surface area of composite object = Surface area of 2 prisms - 2(Area of overlap)


cm2.

Example 2 Finding the Surface Area of a Composite Object Made

from a Rectangular Prism and a Cylinder

Find the surface area of this object.

Surface area of rectangular prism


Faces Area (cm2)

Front15 cm

Back

Top 12 cm 4(12 X 15) = 720

Bottom

12 cm

Right

Left 12 cm2(12 x 12) = 288

Total 1008


38

ace area of cylinder

itching Faces Diagram Corresponding Area (cm2)

a@ 2cm

2XiTX22=25.13

atom

21x(2) cm

irved surface 10 cm2 x 7r x 2 x 10 = 125.67

)tal150.80

surface area is about 150.80 cm2.

!a of overlap

iagram Corresponding Area (cm2)

lrrX22=12.57

e area of overlap is about 12.57 cm2.

composite object = SA rectangular prism + SA cylinder - 2(Area of overlap)

1008 + 150.80 - 2(12.57)

1133.66

ie surface area is about 1134 cmz.

nk

The diagram shows the surface area of the rectangular

--G 3 cm

prism and cylinder that make up a composite object.


The overlap is a

Area of overlap =cmz

SA = 56.5 cm2


SA composite object = SA

+ SA

- 2(

_

+

-

The surface area of the composite object is about

cmz.

39

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