Question

A rectangle has a length of 11 centimeters and a width of 4.2 centimeters. A circle is drawn inside that touches the rectangle at two points. Which is the closest to the total area of the shaded region?

A. 9.19 cm²
B. 101.59 cm²
C. 60.05 cm²
D. 32.35 cm²

Answer 1

To find the area of the shaded region, subtract the area of the circle from the area of the rectangle.

Step-by-step explanation:

To find the area of the shaded region, we need to subtract the area of the circle from the area of the rectangle. The area of a rectangle is found by multiplying its length by its width. In this case, the length is 11 centimeters and the width is 4.2 centimeters, so the area of the rectangle is 11 cm * 4.2 cm = 46.2 cm².

The area of a circle is found using the formula A = πr², where A is the area and r is the radius of the circle. The radius of the circle is half the width of the rectangle, so r = 4.2 cm / 2 = 2.1 cm. Plugging this into the formula, we get A = π * (2.1 cm)² = 13.86 cm².

Finally, we can calculate the area of the shaded region by subtracting the area of the circle from the area of the rectangle: 46.2 cm² - 13.86 cm² = 32.34 cm².