how do i find the area of a shaded area using pi (3.14)?

Question

I have a square that is shaded and in the middle of the square there is a non-shaded circle. the length is 15 and the width is 15. Please give me clear answers with a description of how you got there. thank you

Answer 1

The aswer to this question is really quite easy.

Since we know that the shaded area is a square, finding its area is a simple matter. Its area is s^2, or s squared, where s is the length of one edge of the square.

To find the area of the circle, we use the fact that for any circle, its area is A = pi x r^2, or pi times r squared, where r is the radius of the circle. To find a circle's radius, measure from the circle's center to any point on the circumference of the circle. Multiply r by itself. Then multiply that result by pi. That gets you the area of the circle.

What you seem to be looking for is the shaded area of the square remaining after removing the area of the circle. To do this, simply subtract the area of the circle from the area of the square.

Your formula should look something like this:

A (shaded) = A (square) - A (circle)
= s^2 - (pi x r^2)

Notice that it does contain the constant pi.

If your circle is tangent to all sides of the square in which it is inscribed (a single point on the circumference of the circle touches each side of the square at its mid-point), then your job is made easier still.

A circle tangent to a circumsribed square (in this case a square constructed outside of the circle) has a radius equal to half the length of a side of the square.

Then the above formula collapses to:

A (shaded) = s^2 - (pi x (s/2)^2)
= s^2 - (pi x (s^2/4))

Note s^2/4 is read s squared divided by four.

Factoring out common factors, we get

A (shaded) = s^2 x (1) - s^2 (pi/4)
= s^2 x (1 - pi/4)

Note that pi/4 is less than 1, so (1 - pi/4) is a positive number.

Hope this helps.

Answer 2

The problem cannot be solve without giving any relationship between the square and the circle.
But I think you're pertaining to a square circumscribed a circle.
That means that the circle is inside the square and the sides of the square intersect the circle.

here's the solution.
all you have to do to get the shaded part is
area of shaded part = area of square - area of circle
A = s^2 - (pi)r^2
The diameter of the circle is equal to the side of the square, therefore the radius of the sircle is half of it and is equal to 7.5

A = 15^2 - (3.14)*(7.5)^2
A = 48.375

Answer 3

area of square = length * length =15 x 15 = 225

area of circle = pi*r^2 = (15/2)^2 x 3.14 =176.625

area of shaded area = area of square - area of circle
= 225 - 176.625 = 48.375

Answer 4

You didn't say anything about the radius of the circle. However the solution method is simple: subtract the area of the circle (which is given by πr², where r is the radius) from the area of the square (which is simply b², where b is the width of the square)

Answer 5

I have to assume the circle touches all four sides of the square. to find the area of teh shaded portion you have to find the area of teh square and then subtract the area of the circle which is where pi comes in.

Square's area = 225 sq units

the radius of the circle is 7.5. to find the area. you have to multiply 3.14 times 7.5 times 7.5

Circle's area = 176.625

Shaded area is 225-176.625=48.375

Whenever you need to find the area of a shaded portion think of it as finding the area of teh larger figure and subtracting the area of the smaller one.

Answer 6

abc is a square of side 10 centimeters and be=ec find the area of the shaded trigle