Question

When AG = 16 ft, find the area of the region that is NOT shaded. Round to the nearest tenth.

Choices:
666.9 ft2
200.9 ft2
731.2 ft2
136.9 ft2

Answer 1

Here's a picture of the circle.

Answer 2

Doe's anyone know how to set up the problem with an equation?

Answer 3

AG = GB = 16
1/2 *16*16 = area of triangle AGB

Answer 4

AG is a radius of the circle. \(\triangle AGB\) is a Right Triangle. It is also isosceles.

Lots of stuff to know about it.

Answer 5

I get the part with the area.

Answer 6

I don't know about the triangle part.

Answer 7

Is it 136.9 ft2?

Answer 8

Here is one silly idea you could try :)
Subtract the `area of this square` from the `area of the circle`,
and then take one fourth of that!

\[\Large\rm A=\frac{1}{4}\left(A_{\circ}-A_{\square}\right)\]Just an idea ^^

Answer 9

this is only one approach

Area of complete circle = pi*r^2 and r = AG = 16
Angle AGB = 90° Sector AB = 1/4 of circle
area of sector not shaded = 3/4* pi*r^2 + 1/2 *b*h
for this problem r = b = h = 16
so area not shaded =

Answer 10

Ooo did I steal your thunder? >.< My bad...

Answer 11

@zepdrix that would give the area shaded

Answer 12

Oh not shaded :) lol my bad.

Answer 13

@FacePlant the area not shaded = area of circle - area shaded

Answer 14

\[\Large\rm A_{shaded}=\frac{1}{4}\left(A_{\circ}-A_{\square}\right)\]\[\Large\rm A=A_{\circ}-A_{shaded}\]

Ok I think I fixed it ;d

Too many A's though lol

Answer 15

I'm still kind of confused. ;/

Answer 16

@FacePlant to find the answer to the nearest tenth calculate to 2 decimal places then round up to 1 decimal place.

Answer 17

area not shaded = 3/4 the circle + triangle this will be the same as
area of circle - area of shaded region

Answer 18

what are you still confused about? ask specific let me try and make it clearer

Answer 19

You think you could give me step by step on how to start it?

Answer 20

Sorry if i'm taking kind of long. :/

Answer 21

do you see that
area not shaded = 3/4 the circle + triangle this will be the same as area of circle - area of shaded region

Answer 22

Yeah

Answer 23

I think i remember it now.

Answer 24

I will set up the equation.

Answer 25

now choose one way and then evaluate I did the part circle and add triangle while zepdrix choose the whole circle and minus the shaded should have the same answer whichever one you use.

Answer 26

I got it, and thank you so much! :)

Answer 27

The answer is 200.9 ft2, right?

Answer 28

no problem

Answer 29

let me do it

Answer 30

i got 731

Answer 31

You may have been told to use a specific value for \(\pi\)?

Answer 32

\(\dfrac{3}{4}\pi 16^2 + \dfrac{1}{2}16^{2} = 256\cdot\dfrac{3\pi + 2}{4} = 256\cdot 2.85619449 = 731.18578949\)