So far in Math 9, I have learned about the following:

• Area of 2D shapes
• Area of 3D shapes

Area of 2D shapes

This is a rectangle.

The rectangle has a perimeter; the length of all sides. In this example, 4 centimetres by 2 centimetres.

The lines represent identical edges.

To calculate the perimeter, simply multiply the two unique lengths then add them.

4cm 2 = 8cm

2cm 2 = 4cm

8cm + 4cm = 12cm

The perimeter is 12 centimetres. We want the area, however. To calculate that, we multiply the unique lengths together. The expression to find area is: , where A is area, B is base (width/length) and H is height. In this case, B is 4cm and H is 2cm.

4cm 2cm = so the area is

The area of all shapes is squared, or to the power of two.

Slanted rectangles, like this one…

…would be calculated with the height being the length of the space between the two parallel horizontal edges.

This here is a triangle with a base of 7cm and height of 8cm.

We continue to use , except we divide A by 2, as triangles are, in fact, half of a rectangle. In this case, B is 7cm and H is 8cm.

7cm 8cm =

2 =

Alas, the area is

This is a circle with a diameter of 10cm.

The area of a circle is calculated using A=πr, π hereafter being referred to as pi. R is the radius of the circle, which we don’t have, only the diameter. To get the radius is easy however; divide the diameter by 2.

10cm 2 = 5cm

Now, we multiply it by pi and square it.

5cm π = about 16cm

If you only have a fraction of a circle, divide the area by the fraction denominator. For example, if you had of a circle, you’d divide by 8.

This rectangle 12cm by 6cm has a circular cutout.

In this case, we would calculate the area of the rectangle and the circle cutout normally.

12cm 6cm = 72cm

6cm 2 = 3cm

3cm π = about 9cm

Now, we subtract the area of the circle from the rectangle.

72cm – 9cm = 63cm

Area of 3D shapes

These are some examples of 3D shapes.

For the purposes of this blog post, each face of each individual cube part represents one unit.

To calculate the surface area of these objects, you’d need to count each unit on the surface of the shape. Alternatively, if you know the area of each face, you can add all of that together.

With the cube (first image, left side) that has 3 by 3 unit/9 square unit faces, you know that each face is the same, so if you multiply 9 by 6 (the amount of faces on the cube) you can determine that the surface area is 81 square units.

With the second object, (first image, right side) there are 9 extra cubes, making for 4 4 by 3 unit/12 square unit faces and 2 3 by 3 unit/9 square unit faces. Multiply each unique face by the number of identical faces, then add the sum together to get the overall surface area, which is 62 square units.

With the third object, (second image) you’ll need to count each square unit.

If you removed a corner from, let’s say, the cube, there won’t be any change in surface area. This is because you are removing three square units, but at the same time, adding another three from the adjacent cubes. However, if you removed a row, you would lose 2 square units from the surface area, as one of the adjacent cubes that would remedy the surface area is now missing. If you removed a single unit from the centre of a face, you would gain 4 extra faces due to the adjacent faces.

Expect updates to this post in the near future.