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Chrissy is making a bird box for her backyard. What is the Surface area of the nesting box, including the hole? What is the surface area of the width of 7.5 inches is doubled? What is the surface area of the width 7.5 inches is half as great? L=5.5in., W=7.5in., H=9in.

Chrissy is making a bird box for her backyard What is the Surface area of the nesting box including the hole What is the surface area of the width of 75 inches class=

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calculista

Answer:

Part a) [tex]SA=316.5\ in^2[/tex]

Part b) [tex]SA=534\ in^2[/tex]

Part c) [tex]SA=207.75\ in^2[/tex]

Step-by-step explanation:

Part a) Find out the surface area

The surface area of a rectangular prism is equal to

[tex]SA=2B+PH[/tex]

where

B is the area of the base

P is the perimeter of the base

H is the height of the prism

Find the area of the base B

[tex]B=(5.5)(7.5)=41.25\ in^2[/tex]

Find the perimeter of the base P

[tex]P=2(5.5+7.5)=26\ in[/tex]

we have

[tex]H=9\ in[/tex]

substitute the values in the formula

[tex]SA=2(41.25)+26(9)[/tex]

[tex]SA=316.5\ in^2[/tex]

Part b) What is the surface area if the width of 7.5 inches is doubled?

we have that

The new width is 2(7.5)=15 in

Find the area of the base B

[tex]B=(5.5)(15)=82.5\ in^2[/tex] ---> the area of the base is doubled

Find the perimeter of the base P

[tex]P=2(5.5+15)=41\ in[/tex]

we have

[tex]H=9\ in[/tex]

substitute the values in the formula

[tex]SA=2(82.5)+41(9)[/tex]

[tex]SA=534\ in^2[/tex]

Part c) What is the surface area if the width 7.5 inches is half as great?

we have that

The new width is 0.5(7.5)=3.75 in

Find the area of the base B

[tex]B=(5.5)(3.75)=20.625\ in^2[/tex]

Find the perimeter of the base P

[tex]P=2(5.5+3.75)=18.50\ in[/tex]

we have

[tex]H=9\ in[/tex]

substitute the values in the formula

[tex]SA=2(20.625)+18.50(9)[/tex]

[tex]SA=207.75\ in^2[/tex]

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