Comparing Area and Perimeter

When measuring shapes, it is easy to mix up area and perimeter. However, they measure two completely different things!

• Perimeter is the distance around the outside of a shape. Think of it as the fence around a garden.
• Area is the amount of space inside a shape. Think of it as the grass growing inside the garden.

Same Perimeter, Different Areas

Can two shapes have the exact same distance around the outside, but hold a different amount of space inside? Yes!

Let's look at two rectangles that both have a perimeter of $20$:

Rectangle 1: A $2 \times 8$ rectangle

• Perimeter: $2 + 8 + 2 + 8 = 20$
• Area: $2 \times 8 = 16$ square units

Rectangle 2: A $4 \times 6$ rectangle

• Perimeter: $4 + 6 + 4 + 6 = 20$
• Area: $4 \times 6 = 24$ square units

Even though the "fence" is the same length, the $4 \times 6$ rectangle gives you much more "grass" inside.

Same Area, Different Perimeters

Shapes can also take up the exact same amount of space but have different distances around their edges.

Let's find two rectangles that both have an area of $12$:

Rectangle A: A $3 \times 4$ rectangle

• Area: $3 \times 4 = 12$ square units
• Perimeter: $3 + 4 + 3 + 4 = 14$

Rectangle B: A $2 \times 6$ rectangle

• Area: $2 \times 6 = 12$ square units
• Perimeter: $2 + 6 + 2 + 6 = 16$

Both shapes have the same area, but Rectangle B requires a longer "fence" to go all the way around it.

Comparing Shapes

Sometimes you just need to calculate and compare to see which shape is bigger.

Question: Which has a greater area: a $3 \times 6$ rectangle or a $4 \times 5$ rectangle?

1. Find the area of the first rectangle: $3 \times 6 = 18$
2. Find the area of the second rectangle: $4 \times 5 = 20$

The $4 \times 5$ rectangle has a greater area ($20 > 18$)!