A complex shape is an irregular shape that is a combination of more than one type of regular shape.
Examples of regular shapes are squares and rectangles.
A complex shape can be a combination of two rectangles, or a rectangle and a square, or even two rectangles and one square.
There are many possible combinations.
In this lesson, we're going to explore how to find their perimeter and area.
Perimeter is the total length around a shape.
To find the perimeter of a complex shape, we just add up the length of all the sides.
What's the perimeter of this shape?
First, we take note of the length of each side.
We add up the lengths of each side.
11 + 3 + 4 + 9 + 7 + 12 = 46
The perimeter of this shape is 46.
Area is the amount of space that a shape covers.
The area of a shape has to do with the space inside it.
To find the area of a complex shape, we need to split the complex shape into smaller, regular shapes like squares and rectangles.
How can we find the area of this park?
First, we split it up into simpler shapes.
Now, we have two shapes.
The top shape is a rectangle.
What are its dimensions?
Its width is 7 km and its height is 2 km.
The bottom shape is a square.
Its sides are all 5 km long.
Let's find the area of the rectangle first.
2 × 7 = 14
The rectangle has an area of 14 km² (square kilometers).
Then, we find the area of the square.
5 × 5 = 25
The area of the square is 25 km² (square kilometers).
Now, we add the two areas, to get the area of the whole park.
14 + 25 = 39
The area of the park is 39 square kilometers (or 39 km²). ✅
What's the area of this swimming pool?
First, you have to figure out how to split it up.
One way is to split it up into 3 rectangles.
- Another way is to split it up into 2 rectangles.
Which way is easier to do?
Yes, the second one. Because then we only have to deal with two shapes.
Let's find the pool's area using that way.
Take a look at the dimensions of the two rectangles:
Tip: We didn't know the length of the longer side of the second rectangle, so we had to add the lengths of the sides that we knew.
To find the area of the first rectangle, multiply 8 m by 9 m:
8 × 9 = 72 m²
To find the area of the second rectangle, multiply 6 m by 16 m:
6 × 16 = 96 m²
Now, we add the two areas together:
72 + 96 = 168 m²
The area of the swimming pool is 168 square meters (or 168 m²). ✅
Great job learning to find the perimeter and area of complex shapes.
Now, complete the practice to master the skill on your own.