Perimeter, area, and volume

Perimeter

The perimeter is the total distance around the outside of a shape.
To calculate the perimeter of a rectangle or square, add the lengths of all the sides together.
The perimeter of a triangle is the sum of the lengths of its three sides.
The perimeter of a circle, also known as the circumference, can be calculated using the formula 2πr where r is the radius of the circle.

Area

Area is the amount of space inside a shape.
The area of a rectangle is calculated by multiplying its width by its height (width × height).
For a square, you simply square the length of one side (side²).
The area of a triangle is given by 1/2 base × height.
The area of a circle is given by the formula πr², where r is the radius.
For a parallelogram, the area is given by the formula base x height.
The area of a trapezium is given by the formula 1/2 (a + b) x h where a and b are the lengths of the parallel sides and h is the height.

Volume

Volume is the amount of space that a three-dimensional object takes up.
For a solid cube or a cuboid, volume is calculated by multiplying length, width, and height together (length × width × height).
The volume of a cylinder is calculated by multiplying the area of the base (which is a circle) by the height: πr²h.
The volume of a cone is given by 1/3πr²h where r is the radius of the base and h is the height.
The volume of a sphere is given by 4/3πr³ where r is the radius.
A prism has the same cross section throughout its length. The volume of a prism is the cross-sectional area multiplied by its length.

Remember that understanding these fundamental concepts about perimeters, areas and volumes will be essential for handling a wide variety of geometry problems. Always keep these formulas at your fingertips.