Question

In the figure above, a square is circumscribed around a circle with a diameter of 20 cm. Points Q, R, S, and T are the midpoints of the square’s sides. What is the total area, in cm², of the shaded regions?

See attachment.

Answer 1

@phi @jim_thompson5910 i don't understand any of this question so please make it as simple as possible.

Answer 2

you have to work at this one. the radius is 1/2 of the diameter. what is the radius ?

Answer 3

10

Answer 4

next, you should know the area of a circle. See
http://www.mathgoodies.com/lessons/vol2/circle_area.html

can you find the area of the circle ?

Answer 5

\[A=\pi*r ^{2}\]

Answer 6

so A=3.14*10^2

Answer 7

yes, what number is that ?

Answer 8

314

Answer 9

make a note of that: area of the circle is 314.

what fraction of the whole circle is the shaded area inside the circle ?

Answer 10

1/4

Answer 11

yes, we know it is 1/4 because QS and RT are diameters and cut the square into 4ths and also the circle into 4ths.

so what is the area of 1/4 of this circle ?

Answer 12

if the whole circle has area 314, what is 1/4 of the circle's area ?

Answer 13

\[314\div4=78.5\]

Answer 14

so that is part of the answer.

now we need the shaded area on the outside of the circle

Answer 15

that is 1/4

Answer 16

to find it, let's find the area of the square. what is the area of this square?
here is a link to lots of area formulas
http://www.mathsisfun.com/area.html

Answer 17

Area = a^2
a = length of side

Answer 18

yes. look at the picture. if QS is 20, what do you think the side of the square is ?

Answer 19

20

Answer 20

and the area of the square is ?

Answer 21

20?

Answer 22

Area = a^2
a = length of side

Answer 23

so A=20^2

Answer 24

yes, and what number is that ?

Answer 25

400