A rectangle as shown has a length of 0.8 cm and a width of 1.2 cm. Six congruent circles, that each touch the rectangle at two points, are drawn inside the rectangle. Which is closest to the area of the shaded region in the rectangle?
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0.96 square meters
0.83 square meters
0.75 square meters
0.21 square meters
The area of the shaded region can be calculated by subtracting the combined area of the six circles from the area of the rectangle.
Area of rectangle = length x width = 0.8 cm x 1.2 cm = 0.96 square cm
Each circle has a radius of 0.4 cm (half the side length of the rectangle) and area = πr^2 = π(0.4)^2 = 0.16π square cm
Combined area of six circles = 6 x 0.16π = 0.96π square cm
Area of shaded region = Area of rectangle - Combined area of six circles
= 0.96 - 0.96π ≈ 0.83 square cm
Therefore, the answer closest to the area of the shaded region in the rectangle is:
0.83 square meters.