"Math Salamanders Free Math Sheets"
Welcome to the Math Salamanders' Geometry Formula Sheet area.
Here you will find a range of different Geometry formulas for 2d and 3d shapes.
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Geometry Formula Sheet
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° 
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 a^{2} + b^{2} = c^{2} 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
The Cosine rule a^{2} = b^{2} + c^{2}  2bc cos A

For more Geometry formulas about triangles, including examples showing the sine and cosine rules, use the link below.
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 = πr^{2} 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:
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:
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. 
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. 
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 nsided regular polygon is:
Interior angles add up to (n2) x 180°
Each angle must be 180(n2)°/n
Geometry Formula Sheet  3D Shapes
Cubes

Volume of a cube: = a x a x a = a^{3} Surface area of a cube: = 6a^{2} 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:
 
Cylinder

Volume of a cylinder = πr^{2}h Surface area of an open cylinder: = 2πrh Surface area of a closed cylinder: = 2πrh + 2πr^{2} = 2πr(r+h) where r is the radius of the cylinder and h is the height. 

Cone

Volume of a cone
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): = πr^{2} + πrs Surface area of a cone (excluding base): = πrs 

Square Pyramid

Volume of a square pyramid
Surface area of a square pyramid (including base): = b^{2} + 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. 
Geometry Cheat Sheets
Here you will find a range of geometry cheat sheets to help you answer a range of geometry questions.
The sheets contain information about angles, types and properties of 2d and 3d shapes, and also common formulas associated with 2d and 3d shapes.
Included in this page are:
Using the sheets in this section will help you understand and answer a range of geometry questions.
List of Geometric Shapes
Here you will find a List of different Geometric Shapes. There are also properties listed about each shape.
Included in this page are the following shapes:
3D Geometric Shapes  Nets
Here you will find our range of Free Nets for 3D Shapes.
The following printables contain nets of common 3D shapes that your child should know. Each net sheet is available both with and without tabs to aid sticking together.
Using these sheets will help your child to:
All the free Printable Geometry Workheets in this section support the Elementary Math Benchmarks.
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