The figure blow shows to have circles at the ends of a rectangle with the dimensions shown Which is closest to the area of the figure and square inches
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To determine the area of the figure, we need to calculate the area of the rectangle and the areas of the two circles.
First, let's find the area of the rectangle. We are given the dimensions of the rectangle in the figure. Let's assume the length of the rectangle is L and the width is W. From the figure, we can determine that:
Length (L) = 12 inches
Width (W) = 6 inches
To calculate the area of a rectangle, we use the formula:
Area of rectangle = Length × Width
Substituting in the values we have:
Area of rectangle = 12 inches × 6 inches = 72 square inches
Next, let's find the areas of the two circles. We need the radius of each circle to calculate its area.
From the figure, we can see that the diameter of each circle is equal to the width of the rectangle. So, the radius (r) of each circle is half the width (W/2).
Radius (r) = Width (W) / 2 = 6 inches / 2 = 3 inches
To calculate the area of a circle, we use the formula:
Area of circle = π × (radius)^2
Substituting in the radius value:
Area of each circle = π × (3 inches)^2
Now we need to determine the value of π (pi), which is a constant approximately equal to 3.14159.
Finally, we can calculate the area of each circle:
Area of each circle ≈ 3.14159 × (3 inches)^2 ≈ 3.14159 × 9 square inches ≈ 28.27 square inches (rounded to two decimal places)
Finally, to determine the approximate area of the figure, we add the area of the rectangle to the sum of the areas of both circles:
Approximate area of the figure = Area of rectangle + 2 × Area of each circle
Approximate area of the figure ≈ 72 square inches + 2 × 28.27 square inches
Approximate area of the figure ≈ 72 square inches + 56.54 square inches
Approximate area of the figure ≈ 128.54 square inches (rounded to two decimal places)
Therefore, the closest value to the area of the figure is approximately 128.54 square inches.