Perimeter and area are two different things. But they're both related to a rectangle's length (or height) and width. Understanding that can be really useful in life.
Tip: this lesson is pretty long. Do your best to soak it up! 🤓
Perimeter is the length or distance around a shape or space.
To find the perimeter of a shape or space, simply add the lengths of all the sides.
Whether there are 3 sides, 4 sides, 5 sides...or more. Just add all of them.
Area is the space taken up by a flat shape.
To find the area of a rectangle, multiply its width by its height.
Two rectangles can have the same perimeter, but different areas.
Great job reviewing! 🎊
Now let's practice solving problems using area and perimeter.
The shapes below have the same perimeter, but different area.
What is the area of rectangle B?
👉 Start by using the information we already know.
We have the height and width of Rectangle A. We can use these to find its perimeter.
We do that by adding the length of all its sides.
4 + 4 + 3 + 3 = 14 meters
This means that the perimeter of Rectangle B is also 14 meters.
We can't figure out the area of B yet because the length of one side is still missing. 😐
How do we find the missing side? 🤔
👉 We work with the side that we know.
We know that the width is 2 meters.
Since opposite sides are equal, we double that to get the sum of two sides.
2 + 2 = 4
Now, we subtract the sum we got from the total perimeter.
14 - 4 = 10
This means that the sum of the two unknown sides is 10 m. 👍
We divide it by 2, to get the length of each unknown side.
10 ÷ 2 = 5
👍 Now we know that the height of Rectangle B is 5 meters!
Since we know the height and width of Rectangle B, we can finally find its area.
This is easy, we just multiply:
2 x 5 = 10 m²
✅ The area of Rectangle B is 10 square meters (or 10 m²).
The rectangles below have the same area, but different perimeter.
👆What is the perimeter of Rectangle A?
👉 To find the perimeter of a rectangle, we need to know its height and width.
We only know the width of Rectangle A - its height is missing!
How do we figure out its height? 🤔
By using the information we have from Rectangle B.
We know that the area of the two rectangles are equal. If we figure out the area of Rectangle B, then we already know the area of Rectangle A.
The formula for area is height x width.
Let's use that now:
5 x 6 = 30 in²
Rectangle B's area is 30 in².
👍 That means Rectangle A's area is also 30 in².
👉 Our next step is to find Rectangle A's missing side. We do this by using the information we already have.
We know that the width of Rectangle A is 3 inches, and its area is 30 in².
Our formula is:
H x W = Area
So, let's fill in our formula with numbers:
H x 3 = 30
Do you remember how to solve an equation with a variable? This is just like that. 😃
Our variable is H (for height). We need to get it alone on the left side.
To do that, we need to cancel out the multiplication on the left side by using division.
We divide both sides by 3!
Remember, what you do on one side should be done on the other side too. This will keep the equation balanced.
H x 3 ÷ 3 = 30 ÷ 3
H = 10 inches
The missing side is 10 inches.
We know that this is correct because when we multiply the two sides to get its area, we get 30 in². 👍 This matches the area of Rectangle B!
👉 Now, we find its perimeter.
This is easy. We just add all the sides.
Remember, the opposites sides of a rectangle are always equal.
This means we double the height, and also the width.
3 + 3 + 10 + 10 = 26 inches
✅ The perimeter of Rectangle A is 26 inches.
Great job! Now, try the practice exercises. 💪