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Course: Staging content lifeboat > Unit 3

Lesson 2: Middle school articles
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Staging content lifeboat
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Middle school articles
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Area of circle

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Item 1

Lucy wants to calculate the area of a 14-in pizza, but she forgot the formula for the area of a circle. She decides to cut the pizza into slices and rearrange the slices so that half the slices point downward and half point upward to form a parallelogram. Since the pizza-circle and the pizza-parallelogram are made up of the same slices, the area of the two figures is the same.
Complete the sentences with the missing values.
Give exact answers.
  • Since the slices come from the pizza, the height of the bumpy parallelogram is approximately the same as the radius of the pizza. So we can approximate that h=r=
     in.
  • The length of the base of the parallelogram is approximately equal to half of the circumference of the pizza: b=C2=
     in.
  • The area of a parallelogram is equal to the length of its base times its height: A=b×h. The area of the pizza is, therefore, A=
    in2.
A pizza of radius r, diameter d=2r, and circumference C=2πr is cut into 12 slices. The slices are then placed so they form a shape that resembles a parallelogram. Since the circle and the parallelogram are made up of the same slices, the area of the two figures is the same.
In the new arrangement of the slices, the crust of the pizza forms the bottom and top edges of the parallelogram.
Complete the sentences with the missing values.
  • The base b of the parallelogram is approximately equal to half of the circumference of the pizza: b=
    .
  • The height h of the parallelogram is approximately equal to the length of the pizza slices: h=
    .
  • Using the formula for the area of a parallelogram, A=b×h, we find the area of the pizza is A=
    .
A circle with diameter d=6 is cut into twelve slices. The slices are then rearranged so that half of the slices point downward and half point upward to form a shape that resembles a parallelogram. Since the circle and the parallelogram are made up of the same slices, the area of the two figures is the same.
Complete the sentences with the missing values.
Give exact answers.
  • The radius of the circle is r=
    .
  • Since the slices come from the circle, the height of the bumpy parallelogram is about the same as the radius, so h=
    .
  • Half the edges of the slices form the base of the parallelogram, so the length of the base is about half the circumference, which means b=
    .
  • Using the formula for the area of a parallelogram, we find the area of the circle is equal to A=b×h=
    .

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