Areas of Composite Shapes

Today we still looked at areas, however we were looking at the area of composite shapes. A composite shape is an irregular shape that is made up of 2 or more regular shapes stuck together (or cut out). For example:

This is a composite shape, because it is made of 2 regular shapes. It has a rectangle with a triangle stuck to the right hand side of it. We know how to find the area of a rectangle and we also know how to find the area of a triangle, so to find the total area of this shape, we find the areas of the 2 regular shapes and add these together. 

So working this out, the area of a rectangle is length times width, so the area of this rectangle is       12 x 14 = 168 centimeters square. The area of a triangle is (base times height) divided by 2, so the area of this triangle is (8 x 12)/2 = 48 centimeters square. So the total area of this shape would simply be the area of the triangle plus the area of the rectangle, which would be 48 + 168 = 216 centimeters square. 

We do have some more complicated shapes. For example, we may have: 

The easiest way to do this one is to break it into 3 rectangles, and find the area of these three rectangles, then add the areas together. I would break it up like so: 

Now we need to find the area of each of the rectangles. 

First we will look at rectangle 1: The are of this one will simply be 12 x 4 = 48 meters square. 

Now looking at rectangle 2: This one is a little more complicated. We are told one of the side lengths, but we don't know the other. We can work this out however. We know the whole left hand side is 12m, and we know that there is 4m above rectangle 2, and 5m below it. So this means that the total side length must be 12 - 4 - 5 = 3m. So we can now work out the area of this rectangle. It would be     5 x 3 = 15 meters square. 

Finally rectangle 3: This one is a little easier. We know the height is 12m and the width is 3m so the area will be 12 x 3 = 36 meters square. 

Now that we know all the area of all of our rectangles, we can find the area of the whole shape. This will be 48 + 15 + 36 = 99 meters square. 

You should now be able to work through the rest of the worksheet on area. Try and have all of this finished by Tuesday. Remember to do all of the questions on this sheet. 

As always, feel free to comment on here if you have any questions, or email or chat to me in person.