Question

In the figure above, the circle with the center O is inscribed in square WXYZ. What is the area of the shaded portion of the figure?

Answer 1

this is the pic

Answer 2

@Loser66

Answer 3

@TheSmartOne

Answer 4

If you take the circle away from the square you will be left with four corner triangular shapes. Can you see what fraction of this remaining area is represented by the shaded regions in your diagram?

Answer 5

um not really

Answer 6

look at the shapes carefully

Answer 7

look at the bottom left shaded area - can you see that this represents half of the corner triangular piece?

Answer 8

yes

Answer 9

similarly, the right shaded area represents half of that right corner triangular piece - agreed?

Answer 10

yes

Answer 11

therefore, if we take the 2 shaded areas together then they must equal one corner triangular piece.

Answer 12

since all the corner triangular pieces are identical

Answer 13

ok

Answer 14

good - now can you see that we have 4 corner triangular pieces?

Answer 15

yes

Answer 16

and since the shaded area represents 1 corner triangular piece, then the shaded area must equal a quarter of the total area of all the corner triangular pieces - agreed?

Answer 17

yes

Answer 18

so all you need to do now is to find the total area of all the corner triangular pieces

Answer 19

you can get that by subtracting the area of the circle from the area of the square

Answer 20

can you help me on that too? I never learned this

Answer 21

you are given the side length of the outer square - it is shown as 4

so what is the area of this square?

Answer 22

16

Answer 23

good.

now in inner circle touches the sides of the square it is inside, so its diameter is?

Answer 24

idk

Answer 25

what would be the length of the vertical dotted line in this diagram: