Put simply, perimeter is the distance around a shape and area is the amount of space inside of a shape. To get a feel for what that really means we'll need to look at some shapes.
Here's a rectangle.
If we wanted to find the perimeter of this rectangle, that's the distance around, so we would just need to add up all of these sides.
That would be 4 + 6 + 4 + 6 which makes 20. So, the perimeter of the shape is 20.
Area is a little bit more complicated - how do we figure out how much space is inside of something anyway? One way is to break this up into unit squares - 1 by 1 squares - and count.
We could just count these now, but there’s a lot of them. A better way would be it'll see but there are four rows of six each so we can just count by sixes 6-12-18-24. An even better way would be to multiply 4 rows times 6 squares in each row. 6 times 4 is 24.
And that's our first area formula. The area of a rectangle is the length - in this case is 6 - times the width - in this case 4 .
But what if our shape is more complicated? Let's pick something else, like a triangle.
So here’s our triangle. Perimeter for this triangle is just the same - what's the distance around? We just add up all the sides. 6 + 8 + 10 makes 24. Finding the area is a little bit trickier - but we can be a little bit clever. We’re going to draw in this dotted line right here.
This made a rectangle and we already know how to find the area of a rectangle. That’s just length times width, so for us it would be 6 × 8 is 48.
BUT, we don't actually have a rectangle, do we? We have a triangle, but our picture shows that this triangle is half of the rectangle. See how the top triangle and the bottom triangle are the same? So the area of our triangle is going to be half as much as the area of that rectangle. That will be half of 48 which is 24.
That makes another area formula. The area of a triangle is 1/2 times the length times the width - sometimes we call it one half times the base times the height.
But what if our shape is complicated?
The perimeter of all of these shapes is straightforward - just add up all of the sides. But to find the areas, we can always break them up into simpler shapes that we understand.
Then, we can find the areas of the pieces and add them together. Now, there are lots of area formulas for different kinds of shapes to learn, but if we know the basic ideas of breaking up complicated shapes into simpler pieces, we can find the area of anything we want.