Geometry Formula Sheet

1.Geometry Formula Sheet Angles

Angles in a triangle	Angles in a triangle add up to 180° a + b + c = 180°
Angles on a straight line	Angles on a straight line add up to 180° a + b = 180°
Angles around a point	Angles around a point add up to 360° a + b + c + d + e = 360°

2.Geometry Formulas Triangles

Angles in a triangle	add up to 180°
Area of a triangle	Area of a triangle = ½ x b x h or ½bh where b is the length of the base of the triangle and h is the perpendicular height.
Pythagoras’ Theorem	Pythagoras’ theorem a2 + b2 = c2 where a,b and c are the sides of a right triangle. Side c is the hypotenuse (longest side).
Triangle Trigonometry – sin, cos and tan	Basic triangle trigonometry sin θ = o/h cos θ = a/h tan θ = o/a
The Sine and Cosine Rules	The Sine rule  a  sin A =  b  sin B =  c  sin C The Cosine rule a2 = b2 + c2 – 2bc cos A

For more Geometry formulas about triangles, including examples showing the sine and cosine rules, use the link below.

3.Geometry Formula Sheet – Circles

Circumference of a circle The circumference of a circle is the distance all the way around the outside of the circle, or the perimeter of the circle.	The Circumference of a circle = 2πr or πd where r is the radius of the circle and d is the diameter of the circle.
Area of a circle	The area of a circle = πr2 where r is the radius of the circle.
Length of an arc of a circle	The length L of an arc of a circle is: L =  θ  360 2πr where θ is the angle (in degrees) and r is the radius.
Area of an arc of a circle	The area A of an arc of a circle is: A =  θ  360 πr2 where θ is the angle (in degrees) and r is the radius.
Triangle along a semicircle	A triangle drawn inside a circle with one side going along the diameter, and the other 2 sides meeting at any point along the edge of the circle will always make a right angle. The triangle will always be a right triangle.

4.Geometry Formula Sheet – Quadrilaterals

Angles in a quadrilateral	Angles in a quadrilateral add up to 360° a + b + c + d = 360°
Angles in a rectangle	Angles in a rectangle are all right angles (equal to 90°).
Area and Perimeter of a rectangle	Area of a rectangle = a x b Perimeter of a rectangle = 2a + 2b where a and b are the lengths of the two adjacent sides.
Angles in a parallelogram	Angles in a parallelogram opposide angles are equal (opposite sides are also equal). Also, since 2a + 2b = 360°, this means that a + b = 180°.
Area of a parallelogram	Area of a parallelogram = b x h = bh where b is the length of the base, and h is the perpendicular height of the parallelogram.

5.Geometry Formula Sheet – Angles in regular polygons

Equilateral Triangle	Angle: 60° Interior angles add up to 180°
Square	Angle: 90° Interior angles add up to 360°
Pentagon	Angle: 108° Interior angles add up to 540°
Hexagon	Angle: 120° Interior angles add up to 720°
Heptagon	Angle: 128.6° (to 1dp) Interior angles add up to 900°
Octagon	Angle: 135° Interior angles add up to 1080°
Nonagon	Angle: 140° Interior angles add up to 1260°
Decagon	Angle: 144° Interior angles add up to 1440°

A general formula for this rule for an n-sided regular polygon is:

Interior angles add up to (n-2) x 180°

Each angle must be 180(n-2)°/n

6.Geometry Formula Sheet – 3D Shapes

Cubes	Volume of a cube: = a x a x a = a3 Surface area of a cube: = 6a2 where a is the length of each side.
Cuboid	Volume of a cuboid: = length x width x height = lwh Surface area of a cuboid: = 2lw + 2wh + 2lh
Sphere	Volume of a sphere: = 4/3 πr3 Surface area of a sphere: = 4πr2 where r is the radius of the sphere.
Cylinder	Volume of a cylinder = πr2h Surface area of an open cylinder: = 2πrh Surface area of a closed cylinder: = 2πrh + 2πr2 = 2πr(r+h) where r is the radius of the cylinder and h is the height.
Cone	Volume of a cone = 1/3 πr2h where r is the radius of the widest part of the cone, and h is the height of the cone. Surface area of a cone (including base): = πr2 + πrs Surface area of a cone (excluding base): = πrs
Square Pyramid (square-based pyramid)	Volume of a square pyramid = 1/3 b2h Surface area of a square pyramid (including base): = b2 + 2bs Surface area of a square pyramid (excluding base): = 2bs   where b is the length of one side of the base, h is the vertical height of the pyramid and s is the slant height of one of the triangles.
Pyramid (general)	Volume of a pyramid = 1⁄3 (base area x height) = 1⁄3 Ah where A is the area of the base, and h is the height. This formula works for any pyramid with a rectangular or triangular base and triangular sides.