that looks almost like a parallelogram. Sketch her new arrangement. She noticed that the radius of a circle represents the height of the shape. Which measure of the circle describes the length of the base of the parallelogram? Using the formula for the area of a parallelogram and the measures from above, derive the formula for the area of a circle. Show your steps. Use words, numbers, and/or pictures to show your work. 9. Pi Day In this task, you will use measurements and areas of polygons to derive the formulas for the circumference and area of a circle. You can use a ruler to measure distances that are straight, but it is difficult to measure around a circle with a ruler. However, you can do an experiment to find a good approximation of the formula for the circumference of a circle. You can find the area of a rectangle by calculating the number of square units that cover it, but square units do not fit neatly in a circle. However, you can approximate the area of a circle by finding the area of known figures that are close in size. Part A. Use the circular or cylindrical items your teacher provides. Wrap a string around each item and measure the length of string that goes around it. Record this measure as the circumference of the item and include units. Then, use a ruler or yardstick to measure the diameter of the circle. Record your findings in the table below and include units. You may use different units for different items, but be sure that both measurements of each item are in the same units. Be as precise as possible when you are measuring. Part B. In the last column of the table, write the ratio of the circumference
that looks almost like a parallelogram. Sketch her new arrangement. She noticed that the radius of a circle represents the height of the shape. Which measure of the circle describes the length of the base of the parallelogram? Using the formula for the area of a parallelogram and the measures from above, derive the formula for the area of a circle. Show your steps. Use words, numbers, and/or pictures to show your work. 9. Pi Day In this task, you will use measurements and areas of polygons to derive the formulas for the circumference and area of a circle. You can use a ruler to measure distances that are straight, but it is difficult to measure around a circle with a ruler. However, you can do an experiment to find a good approximation of the formula for the circumference of a circle. You can find the area of a rectangle by calculating the number of square units that cover it, but square units do not fit neatly in a circle. However, you can approximate the area of a circle by finding the area of known figures that are close in size. Part A. Use the circular or cylindrical items your teacher provides. Wrap a string around each item and measure the length of string that goes around it. Record this measure as the circumference of the item and include units. Then, use a ruler or yardstick to measure the diameter of the circle. Record your findings in the table below and include units. You may use different units for different items, but be sure that both measurements of each item are in the same units. Be as precise as possible when you are measuring. Part B. In the last column of the table, write the ratio of the circumference
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