Answer:
113.04 cm²
Step-by-step explanation:
Solving the Problem
Understanding the Problem
We're told
- the perimeter of the square is 48 cm
- a circle is inscribed inside the square
and we need to find the area of the circle.
To find the area of a circle we must find its radius, A = r²π.
If we draw a straight line from the center of the circle to the point of the circle directly above it, we can see that the radius is half of the square's side length.
All we have to do is the square's side length.
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Squares and Recalling Perimeter
Perimeter is the sum of all the side lengths of a shape, since a square has equal lengths on all four sides the perimeter for this quadrilateral is 4s, where s is its side length.
We're given the square's perimeter, so equate it and solve for s.
4s = 48
4s / 4 = 48 / 4
s = 12
So, the side length of the square is 12 cm.
This means that half of the square's side length, the radius of the inscribed circle, is 6 cm.
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Finding the Circle's Area
Using the area formula for a circle, our answer is
6²π = 6²(3.14) = 36(3.14) = 113.04 cm².
