After cutting two identical quarter circles from a rectangle with a side length of 12 cm and a radius of 6 cm, the remaining area is approximately 13.38 square centimeters.
The given figure illustrates a rectangle with two identical quarter circles cut from it. The rectangle has a side length of 12 cm, and each quarter circle has a radius of 6 cm. To analyze this geometric configuration, let's calculate the total area of the rectangle and then subtract the areas of the two quarter circles.
The area of the rectangle is given by length multiplied by width, so in this case, it's 12 cm multiplied by 6 cm, resulting in an area of 72 square centimeters. Now, we need to find the area of one quarter circle and then subtract it twice since there are two quarter circles.
The area of a full circle is given by the formula A = πr^2, where r is the radius. For a quarter circle, we divide this area by 4. Thus, the area of one quarter circle is 1/4 π (6 cm)^2 = 9π cm^2.
Since there are two identical quarter circles, the total area they occupy is 2 times 9π cm^2, which is 18π cm^2.
Now, subtracting this from the total area of the rectangle:
72 cm^2 - 18π cm^2 ≈ 13.38 cm^2