Finding area of compound shapes - How to find the perimeter and area of compound shapes

A compound shape is a shape that is made up of other 'basic shapes'; basic shapes are those that we know such as Squares, Rectangles, Triangles, Quadrilaterals, Pentagons, Hexagons etc.

For example, look at an L shape, we can think of it as two rectangles stuck together. 

Thinking of it like this makes it much easier to work out the area and perimeter of the compound shape..

How to find the perimeter of a compound shape. - Examples of compound Perimeter 

The perimeter of a compound shape is the distance around the edge of a shape, you calculate it by adding together the lengths of each side.

Finding the unknown side of a compound shape: If there are unknown lengths within a shape, we can work it out by looking at the other sides.


For example, 

 L shape

The perimeter of this shape is 6+2+3+5+x+y. We must calculate x and y before we can calculate the perimeter.

To calculate 'x':

We know the total height is 6
So, 
3 + x = 6
Thus, x=3

To calculate 'y': 

We know y is the total width of the compound shape.
Thus, y = 2+5 = 7

So the total perimeter of the compound shape is 6+2+3+5+3+7 = 26cm

How to find the Area of a compound shape. - Examples of compound Area

This is when the combination of 'basic shapes' comes in handy. We can break the compound shape into basic shapes, that we know how to calculate the area of, and add these areas together to get the total area of the compound shape.

Using the example above, we can look at the 'L' shape as a a rectangle on top of another rectangle.

The rectangle is 2 by 3 (as labelled), so the area of this square is 6cm2

The rectangle is x by y, which we know is 3 by 7, as calculated above, so the area of the rectangle is 21cm2.

So the total area of the compound shape is 6+21=27cm2

Remember that the unit of lengths is cm and the unit of area is cm2!

 

 

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