2D Shapes and Their Properties

Basic Terminology

A 2D shape is a flat geometric figure with length and breadth, but no depth.
2D shapes have edges, which are the lines that define the shape, and vertices, which are the points where the edges meet.
The perimeter of a shape is the total distance around the edge of the shape.
The area of a shape is the space inside the shape.

A circle is a shape with all points the same distance from the centre. It has no edges or vertices.
A triangle has three edges and three vertices. The sum of the internal angles is 180 degrees.
A rectangle has four edges and four vertices. All angles are right angles, and opposite sides are equal in length.
A square is a special type of rectangle where all sides are equal in length.
A parallelogram has four sides and four vertices. Opposite sides are parallel and equal in length, and opposite angles are equal.
A rhombus is a parallelogram with all sides equal in length.
A trapezium has four sides, with at least one pair of sides parallel.

The perimeter of a shape can be calculated by adding the lengths of all its edges.
The area of a rectangle can be calculated using the formula length x breadth.
The area of a triangle can be calculated using the formula 1/2 base x height.
The area of a circle can be calculated using the formula πr², where r is the radius.
In any triangle, the sum of two sides must be greater than the length of the third side.
In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem.
The sides of a square are all the same length, and the angles are all right angles.
In a rectangle, opposite sides are equal in length and the angles are all right angles.

This overview of 2D shapes and their properties should provide a firm foundation for understanding and working with these shapes in various contexts.