Exploring Perimeter and Area Relationships

The video explores whether figures with the same perimeter can have different areas. Vaughn Crowder demonstrates this concept using two rectangles and a circle, each with a perimeter of 18 inches. The first rectangle has an area of 20 square inches, while the second, longer rectangle has an area of 8 square inches. A circle with the same perimeter has an area of 25.7 square inches. This illustrates that figures with identical perimeters can indeed have varying areas.

What is the perimeter of the first rectangle discussed?

• 18 inches

• 8 inches

• 20 inches

• 25 inches

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CCSS.3.MD.D.8

How do you calculate the area of a rectangle?

• Length + Width

• Length x Width

• Length / Width

• 2 x (Length + Width)

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CCSS.3.MD.C.7B

CCSS.4.MD.A.3

What is the area of the thin rectangle?

• 10 square inches

• 8 square inches

• 18 square inches

• 1 square inch

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CCSS.3.MD.C.6

Can two figures with the same perimeter have different areas?

• Yes, sometimes

• No, only if they are circles

• No, never

• Yes, always

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CCSS.3.MD.D.8

What is the radius of the circle discussed?

• 2.86 inches

• 18 inches

• 25.7 inches

• 1 inch

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CCSS.7.G.B.4

What is the area of the circle with a perimeter of 18 inches?

• 20 square inches

• 8 square inches

• 18 square inches

• 25.7 square inches

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CCSS.7.G.B.4

What term is used to describe the perimeter of a circle?

• Radius

• Circumference

• Diameter

• Arc

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CCSS.7.G.B.4

What does the teacher emphasize about math in the conclusion?

• It is complex

• It is a four-letter word

• It is not a four-letter word

• It is about memorization