GO Math 11.9: Same Perimeter, Different Areas

Front

What is the definition of perimeter?

Back

Perimeter is the total distance around the outside of a shape, calculated by adding the lengths of all its sides.

Front

What is the definition of area?

Back

Area is the amount of space inside a two-dimensional shape, measured in square units.

Front

How can two rectangles have the same perimeter but different areas?

Back

Two rectangles can have the same perimeter if their side lengths are adjusted accordingly, but their areas can differ based on the specific dimensions of the sides.

Front

If Rectangle A has a perimeter of 20 units, what could be the dimensions of another rectangle with the same perimeter but different area?

Back

Possible dimensions could be 6 units by 4 units for Rectangle A and 5 units by 5 units for another rectangle.

Front

What is the formula for calculating the perimeter of a rectangle?

Back

The formula for the perimeter (P) of a rectangle is P = 2(length + width).

Front

What is the formula for calculating the area of a rectangle?

Back

The formula for the area (A) of a rectangle is A = length × width.

Front

Can a rectangle with a perimeter of 20 units have an area greater than 30 square units?

Back

Yes, depending on the dimensions, a rectangle with a perimeter of 20 units can have an area greater than 30 square units.

Front

What is an example of two rectangles with the same perimeter but different areas?

Back

Rectangle 1: 6 units by 4 units (Area = 24 sq. units), Rectangle 2: 5 units by 5 units (Area = 25 sq. units). Both have a perimeter of 20 units.

Front

What happens to the area of a rectangle if you increase one side while keeping the perimeter constant?

Back

If you increase one side while keeping the perimeter constant, the area may increase or decrease depending on the change in the other side.

Front

What is the relationship between the dimensions of a rectangle and its area?

Back

The area of a rectangle is directly related to its dimensions; increasing either the length or width increases the area.