Find the area of the shaded portion in the square. Show all work for full credit.
(Hint: Assume the central point of the arc is the corresponding corner.)
https://wca.sooschools.com/media/g_geo_ccss_2016/8/groupi57.gif
My answer-

We can find the area of shaded region by subtracting area of quarter of circle from the area of square
Let us first find the area of given square.
Side of square=6
Area of square= (side)²
= 6² = 36
Now we are going to find the area of quarter of circle.
Radius of circle = 6
Area of quarter = π/4 (radius)² =3.14/4 x 6²
= 28.27
Hence area of the shaded region = area of square - area of quarter
= 36-28.27 = 7.73

My teacher said-you area of the quarter is where you messed up you set it up correctly but took it somewhere odd your answer is somewhat correct 36- something with pi would have made it correct

Question

Find the area of the shaded portion in the square. Show all work for full credit.
(Hint: Assume the central point of the arc is the corresponding corner.)
https://wca.sooschools.com/media/g_geo_ccss_2016/8/groupi57.gif
My answer-

We can find the area of shaded region by subtracting area of quarter of circle from the area of square
Let us first find the area of given square.
Side of square=6
Area of square= (side)²
= 6² = 36
Now we are going to find the area of quarter of circle.
Radius of circle = 6
Area of quarter = π/4 (radius)² =3.14/4 x 6²
= 28.27
Hence area of the shaded region = area of square - area of quarter
= 36-28.27 = 7.73

My teacher said-you area of the quarter is where you messed up you set it up correctly but took it somewhere odd your answer is somewhat correct 36- something with pi would have made it correct

sammirosesharp · Answer

@563blackghost @Vocaloid

563blackghost · Answer

They wanted it in terms of pi meaning that you would not have incorporated into the simplification.

$\large\bf{A=\pi r^{2} \times \frac{1}{4}}$

$\large\bf{A=\pi \frac{36}{4}}$

$\large\bf{A=9 \pi}$

Everything else is correct but now you need to subtract the two. `area of a square and circle` thus having thus having the answer $\large\bf{36 - 9  \pi}$

563blackghost · Answer

whoops double repeat there...

563blackghost · Answer

What she meant by odd is how you setted up your area of a circle.

You put it as $\Large\bf{\frac{\pi}{4} r^{2}}$ while it is to be $\Large\bf{\frac{r^{2}}{4} \pi}$

563blackghost · Answer

Do you undestand what I mean @sammirosesharp ?

loveboy · Answer

I think for her odd refers to an answer which include pi in it because it requires less calculation.

sammirosesharp · Answer

So I just change it to the r^2/4 pi??? and how would I subtract the two? I'm sorry I dont mean to sound dumb. I literally feel brain fried though.

563blackghost · Answer

Yea I just saw that, but his/her setup is still incorrect.

563blackghost · Answer

You would plug and simplify.

$\large\bf{\frac{6^{2}}{4} \pi \rightarrow 9 \pi}$

Now you know that the area of a circle is `36` and the are of 1/4 of a circle is `9pi` so we subtract the two.

$\large\bf{36-9 \pi}$

You can not simplify this any further.

sammirosesharp · Answer

So would the radius of the circle still be 6 to begin with? I'm trying to change everything around now, just trying to make sure I dont mess up what is correct.

563blackghost · Answer

Yes it would still be 6.

sammirosesharp · Answer

And the area would be r²/4π?

loveboy · Answer

πr²/4 is correct as well :)

563blackghost · Answer

yea that is setup right, though make it noticeable that pi is not being multiplied by 4.

sammirosesharp · Answer

So does this look correct now?
Now we are going to find the area of quarter of circle.
Radius of circle = 6
Area of quarter = r²/4π
Hence area of the shaded region = area of square - area of quarter
=36−9π

563blackghost · Answer

cause that is what it looks like...

have it as (r²/4)π

563blackghost · Answer

add the parenthesis around r²/4 and you should be good to go.

sammirosesharp · Answer

Thank you soo much. You have me in tears for helping me.. omg.

563blackghost · Answer

no problem :D