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What is the total area of this composite figure rounded to the nearest inch?

 May 3, 2016

Best Answer 

 #1
avatar+3451 
+5

So basically what we have here is a rectangle on the bottom part, and then a half circle on the upper part. We'll need to add these two areas together to get the total area.

For the area of the rectangle, simply multiply 6 in times 2 in (base times height), giving you \(12\; in^2\).

For the half circle, we know that the area of a circle is pi times the radius^2. Well, we don't know the radius but we do know the diameter of this circle, which is 6 in. The radius is always half the diameter, so the radius is 3 in.

Meaning, the area of this half circle is 1/2(pi((3 in)^2)) =

\(\frac{9}{2}\pi\; in^2\)

or aproximately 

\(14.13\; in^2\)

Adding these together we get aproximately

\(28.13\; in^2\)

Which, if we're rounding to the nearest inch, would come out to

\(28\; in^2\)

 

 

Thanks for the question dude. If you have any additional questions or don't understand how I did this, or even see a mistake of mine, feel free to let us know and me or another forum member would love to help!

 May 3, 2016
edited by NinjaDevo  May 3, 2016
 #1
avatar+3451 
+5
Best Answer

So basically what we have here is a rectangle on the bottom part, and then a half circle on the upper part. We'll need to add these two areas together to get the total area.

For the area of the rectangle, simply multiply 6 in times 2 in (base times height), giving you \(12\; in^2\).

For the half circle, we know that the area of a circle is pi times the radius^2. Well, we don't know the radius but we do know the diameter of this circle, which is 6 in. The radius is always half the diameter, so the radius is 3 in.

Meaning, the area of this half circle is 1/2(pi((3 in)^2)) =

\(\frac{9}{2}\pi\; in^2\)

or aproximately 

\(14.13\; in^2\)

Adding these together we get aproximately

\(28.13\; in^2\)

Which, if we're rounding to the nearest inch, would come out to

\(28\; in^2\)

 

 

Thanks for the question dude. If you have any additional questions or don't understand how I did this, or even see a mistake of mine, feel free to let us know and me or another forum member would love to help!

NinjaDevo May 3, 2016
edited by NinjaDevo  May 3, 2016
 #2
avatar+23566 
+5

NinjaDevo's METHODOLOGY is correct, bu there is an error in the CALCULATION 

9/2 pi = 14.137      TRUE !

Now add 12         14.137 + 12 = 26.137   ~=26       NOT  28   !

 May 3, 2016

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