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

Guest May 3, 2016

#1**+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!

NinjaDevo May 3, 2016

#1**+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

#2**+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 !

ElectricPavlov May 3, 2016