# Shapes and area

### Shapes and area

Triangles can be defined by the length of their sides or by their angle types.

Scalene triangles are where none of the sides are equal. Isosceles triangles are where at least two of the sides have equal length. Equilateral triangles have all three sides of equal length.

All triangles have three angles adding to 180°.

Acute triangles are where all three angles are less than 90°. Right triangles have one angle which is exactly 90°. Obtuse triangles have one angle which is greater than 90°.

Polygons are any shape with at least three straight sides and angles, typically five or more. A ‘regular polygon’ is equilateral (all sides have the same length) and also has all angles equal in measure.

Quadrilaterals are polygons with four sides and four corners. Therefore all squares and rectangles are quadrilaterals. Parallelograms are quadrilaterals with two pairs of parallel sides.

The perimeter is the length of an outline of a shape, calculated by adding together the length of each side.

The area of a rectangle is measured in square units, which could be square inches, square feet, square metres, etc. The calculation is simply length multiplied by width, represented by A = L * W.

The area of a triangle can be calculated using an adapted version of the formula for the area of a rectangle. If you copy a triangle, flip it 180° and place it next to the original you end up with a parallelogram, a type of rectangle. You need to half the ordinary rectangle calculation, because you only want the area of the triangle. Therefore the formula is half the base multiplied by the height, A = W * 0.5 * L.

To calculate the area of a circle you first need to be able to understand and define the following:
Radius – The distance from the centre of a circle to the edge
Diameter – The full width of a circle
Circumference – The distance around the circle
Pi – The ratio of a circle’s circumference to its diameter, which is 3.14159265.

The area of a circle is calculated as pi multiplied by the square of the radius: A = π * r^2.

Pythagoras’ theorem can be used when we know two sides of a triangle in order to calculate the third side. Pythagoras discovered that on a right triangle, the square of the hypotenuse (the side opposite the right angle, which is always the longest side) is equal to the sum of the squares of the other two sides a^2 + b^2 = c^2.