Perimeter and Area

Perimeter

Perimeter is the total distance around the edge of a 2D shape.
For a rectangle, the perimeter is calculated as 2(width + length).
For a square, all sides are equal, so the perimeter is 4 x side length.
For a circle, the perimeter is commonly known as the circumference and it can be calculated using the formula 2πr where r is the radius of the circle.
If a shape is irregular, add up the lengths of each side to find the perimeter.
Remember that the perimeter is a length, so it should be in units such as cm, m, km, etc.

Area

Area refers to the amount of space inside a 2D shape.
The area of a rectangle can be calculated by width x length.
For a square, since all sides are equal, the area is calculated as side length^2.
The area of a circle is given by the formula πr^2, where r is the radius.
The area of a triangle is 1/2(base x height).
The area of a trapezium is given by the formula 1/2(a+b)h, where a and b are the lengths of the parallel sides and h is the height.
Remember that the area is always measured in square units such as cm^2, m^2, km^2 etc.
For irregular shapes, try to divide the shape into simple, regular shapes, then add up the area of these individual parts.

Composite Shapes

Composite shapes are shapes made up of simpler shapes.
To find the perimeter of a composite shape, add up the lengths of all its outer sides.
To find the area of a composite shape, divide the shape into simpler shapes for which you know how to calculate the area, calculate the area of each of these, then add up the results.
Be careful with composite shapes - remember to subtract the area of any ‘holes’ (e.g. if the composite shape is ‘L’-shaped or if it has hollow sections).

Volume

Volume measures the space that a 3D shape occupies.
The volume of a cuboid can be calculated as length x width x height.
The volume of a cube (all sides equal) is side length^3.
The volume of a cylinder can be found using the formula πr^2h, where r is the radius of the base and h is the height.
Unlike area and perimeter, volume is always measured in cubic units, such as cm^3, m^3, km^3 etc.
In the case of composite shapes, find the volume of each simpler shape separately, then add the results together. Remember to subtract for any hollow spaces.

Conversions between units

When dealing with area and volume, it’s important to remember to convert units so that they are consistent across the problem.
Keep track of whether you’re dealing with lengths (1D), areas (2D) or volumes (3D), and raise conversion factors to the appropriate power.
For example, to convert from m to cm (1D), multiply by 100; to convert from m^2 (2D) to cm^2, multiply by 100^2 (= 10,000); to convert from m^3 (3D) to cm^3, multiply by 100^3 (= 1,000,000).

Remember: Always check your answers, have you used the correct formulas? Are your units consistent and correct? Everything counts when it comes to success in your Shapes and Area tasks!