Exploring Area and Perimeter Differences

The video tutorial explores the concepts of perimeter and area, examining whether shapes with the same perimeter have the same area and vice versa. Through practical examples, it demonstrates that shapes can have the same area but different perimeters and vice versa. The tutorial includes exercises comparing different shapes and solving real-world problems, such as choosing garden layouts and window frames, to reinforce understanding. The lesson concludes with a summary of the key concepts and encourages further exploration of math topics.

Do shapes with the same perimeter always have the same area?

• No, not necessarily

• Yes, always

• Only for circles

• Only for squares

Tags

CCSS.2.G.A.1

How do you find the area of a shape?

• Divide the perimeter by the number of sides

• Add all the sides

• Multiply width by height

• Subtract the smallest side from the largest

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Can two different shapes have the same area?

• No, never

• Yes, always

• Yes, but they will have different perimeters

• Yes, but only if they are rectangles

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CCSS.3.MD.D.8

How do you find the perimeter of a rectangle?

• Add the length to the width

• Multiply the length by the width

• Multiply all sides by two

• Add all sides of the rectangle

Tags

CCSS.4.MD.A.3

If a garden's width is 5 feet and length is 5 feet, what is its area?

• 10 square feet

• 25 square feet

• 15 square feet

• 20 square feet

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

If two gardens have the same perimeter, will they have the same area?

• Only if they are square gardens

• Only if they are circular gardens

• No, the area can differ

• Yes, without exception

Tags

CCSS.3.MD.D.8

Which garden should Sally choose for a larger area?

• Both gardens have the same area

• Garden B with 24 square feet

• Garden A with 25 square feet

• Neither, as they have different perimeters

Tags

CCSS.3.MD.D.8

What is the perimeter of a shape with sides of 4, 4, 2, and 2 feet?

• 10 feet

• 12 feet

• 14 feet

• 16 feet

Tags

CCSS.3.MD.D.8

If a window is 4 feet by 4 feet, what is its area?

• 8 square feet

• 20 square feet

• 16 square feet

• 12 square feet

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

What is the best strategy to save money on fencing for a backyard?

• Choosing the shape with the least sides

• Choosing the shape with the largest area

• Choosing the shape with the most sides

• Choosing the shape with the smallest perimeter