In rectangle PQRS above, arc QT and RT are quarter circles with centers at P and S, respectively. If the radius of each quarter circle is 1, what is the area of the shaded region? (This a problem from the Blue Book, Test 6, Section 2, Question 16 on page 703.)

These problems drive my students crazy.

The trick is to write out a rebus or a map that shows you what you need to do.

## Making apple pie

My little girl can’t read yet so I have to get creative when I put notes in her lunchbox.

Here I’m trying to tell her we will make an apple pie after school.

I will cut up the apples and she will roll out the dough with a rolling pin (a favorite activity) and we will put them together to make apple pie.

## Draw your own rebus

You can use this exactly same strategy to solve funky shape problems.

Area of shaded area = Area of rectangle – Area of left shape – Area of right shape

## Fill in the blanks

Now that we know what we need to do, let’s fill in the spots with numbers.

### Area of rectangle

First, transfer all the info from the text to the picture. Since we know that each radius is one, the length of the rectangle is 2 and the width is 1. So the area is 2 x 1 = 2.

### Area of the quarter-circle

It might help to draw the circles so we can clearly see that we are dealing with quarter circles.

The formula for the area of a circle is pi * r^2. Therefore a quarter circle must be 1/4 of that. So 1/4 * pi *1^2 = 1/4 pi.

### Putting it all together

So, subbing back into our formula:

Area of funky shape = 2 – 1/4 pi – 1/4 pi.

Which simplifies to 2 – 2(1/4) pi or 2 – pi/2.

## Recap

- Transfer all information in the text to the picture
- Draw out your “equation” or rebus
- Solve for each thing you need to figure out
- Put it back into the larger equation
- Solve the whole equation

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