Question

suppose we have a circle with a diameter of 7 units. after measuring, we find that the circumference of the circle is approximately 21.08 units. solve for the area of the circle by completing the informal argument. move the answer choices to the correct places. divide the circle into equal sectors and arrange them in a shape similar to a parallelogram. the base of the \parallelogram\ corresponds to of the circle. for the example, the base has a value of units. the height of the \parallelogram\ corresponds to of the circle. for the example, the height has a value of units. the area of the \parallelogram\ area = base × height, is equal to the area of the

Explanation:

Step1: Recall circle - related formulas

The circumference of a circle is $C = \pi d$ and the area is $A=\pi r^{2}$, where $d$ is the diameter and $r$ is the radius. Given $d = 7$ units, so $r=\frac{d}{2}=\frac{7}{2}=3.5$ units.
When we transform a circle into a parallelogram - like shape, the base of the "parallelogram" is half of the circumference of the circle, and the height is the radius of the circle.

Step2: Calculate the base of the "parallelogram"

The base $b$ of the "parallelogram" is half of the circumference. Given $C\approx21.08$ units, so $b=\frac{C}{2}=\frac{21.08}{2}=10.54$ units. The base of the "parallelogram" corresponds to half of the circumference of the circle.

Step3: Calculate the height of the "parallelogram"

The height $h$ of the "parallelogram" is the radius of the circle. Since $d = 7$ units, $h=r=\frac{d}{2}=3.5$ units. The height of the "parallelogram" corresponds to the radius of the circle.

Step4: Calculate the area of the "parallelogram" (which is equal to the area of the circle)

Using the formula for the area of a parallelogram $A = b\times h$. Substitute $b = 10.54$ units and $h = 3.5$ units. $A=10.54\times3.5 = 36.89$ square units. Also, using the circle - area formula $A=\pi r^{2}=\pi\times(3.5)^{2}\approx3.14\times12.25 = 38.465\approx38.47$ square units (using $\pi\approx3.14$). The small difference is due to rounding in the first method.

Answer:

Base value: 10.54 units (corresponds to half of the circumference); Height value: 3.5 units (corresponds to the radius); Area of the circle (equal to area of the "parallelogram"): approximately 38.47 square units.