Question

The figure shows the blueprint that a contractor uses to design ice-skating rinks. Which expression gives the area of the spectator section shaded in green?

Answer 1

NO FIGURE

Answer 2

Hi, upload a picture..

Answer 3

Ok, are you ready to help me find the solution?

Answer 4

okay

Answer 5

no

Answer 6

well.
You know basic geometric shapes. for example: Squares, circles , triangles, etc.
Do you know the formula used for each of them or not?

Answer 7

yes I do

Answer 8

Good.
The only thing you need to do is recognize the shapes you already know in this picture.
Which shapes do you see there?

Answer 9

umm like a half a rectangle but with a semicircle?

Answer 10

a)x2 – πx2
b)3x + 12πx
c)x2 – 18πx2
d)x2 + 12πx2
there are four answers sorry im telling this now

Answer 11

do you see that the green section is the area of the square less the area of the rink ?

Answer 12

yes i do

Answer 13

It doesn't matter. Choices are not needed here.

Answer 14

The bigger shape is a square. Can you tell me why?

Answer 15

because rectangles are squares thats what i heard my math teacher say

Answer 16

It's because its sides all have the same length -> X

Answer 17

And you said something about a semi-circle. You meant the white part of the area.
Is it a complete circle?

Answer 18

yeah, it does not say if its a semicircle or a complete circle

Answer 19

this is a complete circle:

but what you see in the picture is half of it. isn't it?

Answer 20

yes

Answer 21

Good! so what you see in the picture is HALF A CIRCLE.
You also see a SQUARE.

Now, Don't you have any idea how you can calculate the green area?

Answer 22

not really but i guessing that you need to subtract the semi circle with the square

Answer 23

It's correct.
Actually:
green area = square - half a circle

Answer 24

oh
for real?

Answer 25

Now everything is very easy!
What is the area of that square?

Answer 26

x times x

Answer 27

correct me if im wrong isnt that x^2

Answer 28

correct.

and what is the area of Half A Circle.

Answer 29

?

Answer 30

A = (Pi*r^2)/2

Answer 31

very nice!
and to calculate it you need to know r.
What is r in that picture?

Answer 32

umm the rink?

Answer 33

The diameter of the circle is X.
Can u tell me y?

Answer 34

the radius?
sorry geometry isn't really my thing

Answer 35

:)

Answer 36

Look at this one:

Answer 37

Now can you tell me what is r of the half-circle?

Answer 38

r looks like the radius

Answer 39

yes! because it is Radius and it's equal to x/2

Answer 40

Becky I'm so sorry I need to go out.
But let me tell you one thing. The correct answer is not between the choices.
The correct answer is:
\[x^{2}- \frac{ \pi x^{2} }{ 8 }\]

Answer 41

oh okay thank you

Answer 42

But please try to derive it and when I'm back i'll answer any question you have.
Send me a message or tag me.

Answer 43

okay

Answer 44

Thank you :)

Answer 45

Do Great...

Hey.... Do not give up.
If you can answer this question you can answer to many other geometry questions.

Answer 46

yeah now i think i got it the answer since you divided it by 8 i tried 1/8 and i got it
:)

Answer 47

Thank you so much

Answer 48

You're welcome