Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Area of Shaded Region

Square ABCD has a circle inside. The circle is NOT shaded but Square ABCD is shaded in the left over spaces. The side lengths of the square is 2 by 2. Find the area of the shaded region.

Let me see.

Let A_r = area of shaded rregion.

A_r = area of circle - area of Square ABCD.

Is this the correct set up?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Area of Shaded Region

This sounds just like the question I've just answered.

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: Area of Shaded Region

This sounds just like the question I've just answered.

Bob

Yes but this one is the area of the circle minus the area of the square. Is this correct?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Area of Shaded Region

Oh I get it. And yes the set up is right.

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: Area of Shaded Region

Oh I get it. And yes the set up is right.

Bob

Let's do this. All the shaded region examples are on page 37. Let me know if my set up is right for all 4 problems. Now that you have the same book I have, our journey through this book (NOT EVERY PROBLEM, OF COURSE) has become super easy. Do you agree?

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Area of Shaded Region

Oh I get it. And yes the set up is right.

Bob

Problem 38; page 37.

Let A_r = area of shaded region.

A_r = pi•r^2 - (side of square)^2

A_r = pi(1)^2 - (2)^2

A_r = pi - 4

You say?

Last edited by mathxyz (2024-05-18 03:29:35)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Area of Shaded Region

Thanks for the page reference. That helps a lot.  For this one the square is bigger than the circle so your calculation is the wrong was round. 4 is bigger than 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: Area of Shaded Region

Thanks for the page reference. That helps a lot.  For this one the square is bigger than the circle so your calculation is the wrong was round. 4 is bigger than pi.

Bob

Let me try again.

Problem 38; page 37.

Let A_r = area of shaded region.

A_r = (side of square)^2 - pir^2

A_r = (2)^2 - pi(1)^2

A_r = 4 - pi

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Area of Shaded Region

Correct.

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: Area of Shaded Region

Correct.

Bob

Cool. You see, it's better if we both have a copy of the textbook.