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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Square ABCD

I will need to describe the question since posting photos here with my android A-21 phone is ridiculously stressful.

Square ABCD has a shaded circle inside. The side lengths of Square ABCD is given as 2 by 2. Find area of the shaded region.

Let's get started.

Let A_r = area of shaded region.

A_r = area of Square ABCD - area of circle.

Is this the correct set up?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Square ABCD

This sounds like your next question.  Do you want the bit left after you subtract the circle? This is correct if so.

The diameter = the length os side of the square.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD

This sounds like your next question.  Do you want the bit left after you subtract the circle? This is correct if so.

The diameter = the length os side of the square.

Bob

Picture a circle inside square ABCD. The circle is shaded leaving the upper left, upper right, lower left and lower right corners without a shade.
Is my set up right?

Last edited by mathxyz (2024-05-17 10:03:04)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Square ABCD

Yes that looks right.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Phrzby Phil

Member

From: Richmond, VA

Registered: 2022-03-29

Posts: 50

Re: Square ABCD

You say the circle is shaded, and that you want the area of the shaded part.

So - you want the area of the circle, not the difference between the areas of the square and the circle.

Also, technically, you can calculate this only if the circle is specifically inscribed in the square, not just inside it.  An infinite number of circles of various radii are inside the square.

I'm not being picky here, just using mathematical terminology correctly.

---

World Peace Thru Frisbee

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD

You say the circle is shaded, and that you want the area of the shaded part.

So - you want the area of the circle, not the difference between the areas of the square and the circle.

Also, technically, you can calculate this only if the circle is specifically inscribed in the square, not just inside it.  An infinite number of circles of various radii are inside the square.

I'm not being picky here, just using mathematical terminology correctly.

Let's do this. Do what Bob did.

Freely download Michael Sullivan's College Algebra Edition 9 textbook. You can easily find the textbook with a yahoo or Google search. It's a lot easier for both of us to be on the same page. If you decide to download the textbook, the shaded region examples are on page 37.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD

Yes that looks right.

B

Let A_r = area of shaded region.

A_r = area of Square ABCD - area of circle.

A_r = (2)^2 - pi•(1)^2

A_r = 4 - pi

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Square ABCD

If this is question 37 then you just need the area of the circle ie pi

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD

If this is question 37 then you just need the area of the circle ie pi

Bob

Ok. We can now move on from this shaded region stuff. The next section is a review of factoring.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD

If this is question 37 then you just need the area of the circle ie pi

Bob

Ok. We can now move on from this shaded region stuff.