Find the area of the shaded region... (hope you get it)?

Question

...if inside a circle is a square that has an area of 25... the shaded region is the circle while the unshaded region is the square that each side of it is equal to 5...

Answer 1

Area of circle = pi*r^2. Assuming the circle is the smallest circle that can contain the square, then r = (5sqrt(2)/2.
So area circle = 12.5pi
So shaded area = 12.5pi-25= 12.5(pi-2)
Shaded area approximately = 12.5(1.14) =14.25 units^2

Answer 2

If the corners of the square all lie on the circle, then the diagonal of the square is the diameter of the circle. We can easily calculate what that must be:

d = √(s² + s²) = (√2) s²

Since s = 5, d = √[2 (25)] = √50 = 5 √2

Then the area of the circle is:

A = π r²
A = π [(5 √2) / 2]²
A = (50/4) π
A = (25/2) π

The area of the square is:

A (square) = s² = 5² = 25.

So the shaded region is the area of the circle minus the area of the square:

A (shaded) = (25/2) π - 25
A (shaded) = 25 [(π/2) - 1], which is the answer you need.

Answer 3

So you want to know the area of the shaded area. To find this you need to know the area of the circle and the area of the square. The hint is that the square is inside the circle with area of 25 making the sides of the square 5. Next draw a diagonal across the square and calculate the diagonal. you should get 5 square root of 2 in order words 5*(2)^1/2. Once you know your diagonal divide it by 2 and that's your radius. The area of the circle is pi*r^2. pi = 3.14 multiply by its radius squared. Then subtract the area of the square to the area of the circle and you get the shaded region. you should get something like (25*pi / 2 ) - 25.

Answer 4

actually, we do know the radius of the circle. The area of the square is 25, that means the sides of the square are 5. Notice that the digonal of the square is also the diameter of the circle. Use pythgarean to find the diagonal.

5^2 + 5^2 = c^2
50 = c^2
c = 5sqrt(2)

the radius is 5sqrt(2) / 2

to find the shaded area, subtract the area of the square from the area of the circle

pi * r^2 - 25

now you can do the rest.

Answer 5

The area you seek will be Area of circle minus area of triangle+ area of half circle. The area of the big circle = 5² x 22/7 cm² = 550/ 7 = 78+4/7 cm² The triangle is standing on a semicircle, so you need only half of the above = 39+ 2/7 cm² The triangle is isosceles, if you remember your geometry: Its area will be ½base x perp. ht. = 5x5cm² Take this away from the area of the semicircle 39+2/7 - 25 = 14+ 2/7 cm² If the fractiion bothers you, then 14.2857 cm². When you tackle problems like the above, you have to learn to split the figure into parts with whch you can deal: in the above case, a triangle and a semicircle.

Answer 6

Assuming that the four corners of the square are on the circle, the diameter of the circle is the diagonal of the square. whose side is 5.

The diagonal then is 5√2. the radius of the cricle is 5√2/2

the area then of the circle is π r^2, in this case π(5√2/2)^2
=12.5 π

the area in the circle but outside the square is

12.5 π - 25, square units, of course

Answer 7

Assuming that the tips of the square touch the circle, then the diagonal of the square is the same as the diameter of the circle, and that would be SQRT(5^2 +5^2) = 7.0710678.
The area of a circle is Pi r^2, and the radius is half the diameter, so the circle has an area of 36.269908. Take away the area of the square (25) and you have the area of your "shaded region", the 4 arcs: 11.269908.

Answer 8

Assuming the square in inscribed in the circle, then:
The side of the square is 5
The diagonal of the square = diameter of circle = 5√2
The radius of the circle is then 5√2 / 2
The area of the circle is π(5√2 / 2)^2 = 25π/2
The area of the square is 25
The difference is 25π/2 - 25
= 25(π/2 - 1) ≈ 14.27

Answer 9

Do the vertices of the square lie on the circle? if so...

The radius of the circle (r) is 2.5 * sqrt (2); a 45-45-90 triangle is formed with base r and hypotenuse 5

The area of the circle is pi * (2.5 * sqrt (2))^2
= pi * 12.5 = 12.5 pi = 39.27

The area of the square is 25

The area of the shaded area = area of the circle - area of the square = 39.27 - 25 = 14.27

Answer 10

Without knowing the size of the circle, this problem is impossible to compute. I can only give you an equaion:
π r² - 25, where r is the radius of the circle


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Some people on here think they are so smart figuring out the "radius" of the circle from absolutely no information whatsoever. You cannot solve this with the information given!!! If youre so smart you would realize that. Quit jumping to conclusions about the nature of the problem. No one knows for certain if the square touches the circle... but I shouldnt have to tell a genius that!