Question

I will give a medal!
What is the area of this composite figure?

Answer 1

Lets break this down. We know that there are two circles and one square. Do you know how to find the area of a square and a circle?

Answer 2

yes circle is A=pi*r to the second power
square iis A=h to the second power

Answer 3

Okay. Now use these formulas to figure out the area. But remember that there are two semicircles.

Answer 4

well how?

Answer 5

You want to replace the numbers into the formula.

Answer 6

well there is only two numbers?

Answer 7

For example, we are to look at the square and figure out the area for that one.

So we know that the formula would be:
\[A=s^2\]
Where s means the side.

We also know that the side length of the square is 2. So we can also replace s for 2.
\[A=2^2\]

That makes our area be equal to:
\[A=2\times2 = 4\]

So our area for the square is 2.

Now that is what you can do for the two circles also.

Answer 8

Sorry I meant that the area is actually 4 inches for the square.

Answer 9

well the two halfs make one circle right?

Answer 10

Sure

Answer 11

so the diameter is 2 in right?

Answer 12

Yes

Answer 13

so then we find the area of the circle and add it to the square

Answer 14

Try it out.

Answer 15

thnx it worked

Answer 16

You're welcome :)

Answer 17

can you help me with one more quistion?

Answer 18

Okay.

Answer 19

Use the Pythagorean theorem to find the missing length in the following right triangle.

Answer 20

Do you know what is the Pythagorean Theorem?

Answer 21

Meaning the formula?

Answer 22

no we went over it but i forgot what it is

Answer 23

It is:
\[a^2+b^2=c^2\]

Answer 24

Do you understand this?

Answer 25

kinda but what is a b and c?

Answer 26

b is a variable that stands for one of the legs of the right triangle.
c is the variable that stands for the hypotenuse (the longest side of the right triangle)

Answer 27

so c is the number 50?
and b is the number 48?

Answer 28

Correct. However, remember that you're solving for a. Do you know how to do that?

Answer 29

Here's an easy way with the Pythagorean Theorem:
\[a^2+48^2=50^2\]
Square the numbers and then solve for a.

Answer 30

well for 48 squred i got 2,304
and for 50 squred i got 2,500 what do i do next?

Answer 31

Now you do:
\[a^2+2,304=2,500\]

Answer 32

how do i find a?

Answer 33

Solve for a^2

Answer 34

sorry i actually forgot the simplest !

Answer 35

how do i know what is a?

Answer 36

Well you know that to solve for a, you have to do the inverse operation.