Geometry Formula Sheet

"Math Salamanders Free Math Sheets"

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Welcome to the Math Salamanders' Geometry Formula Sheet area.

Here you will find a range of different Geometry formulas for 2d and 3d shapes.

To view the sheets, simply click on the thumbnail of the free printable Math sheets and a new browser window will open to display a larger version of the sheet.

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To save the sheet directly onto your computer, right-click the large version of this free Math sheet and choose 'Save Image As'.

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Geometry Formula Sheet

Here you will find our support page about different Geometry formulas, including triangles, circles, quadrilaterals and polygons, as well as 3d shapes. Using these sheets will help your child to:

know different geometric formula;
apply a range of formula to solve problems.

All the Math sheets in this section follow the Elementary Math Benchmarks.

Geometry Formula Sheet Angles

Angles in a triangle

$angles in a triangle$

Angles in a triangle add up to 180°

a + b + c = 180°

Angles on a straight line

$angles on a straight line$

Angles on a straight line add up to 180°

a + b = 180°

Angles around a point

$angles around a point$

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

$area of a triangle$

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

$Right triangle labelled$

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

$Trigonometry formulas triangles$

Basic triangle trigonometry

sin θ = o/h

cos θ = a/h

tan θ = o/a

The Sine and Cosine Rules

$Geometry Formula Sheet Sine Rule Cosine Rule$

The Sine rule

sin A

sin B

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.

Geometry Formulas Triangles

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

Is the amount of space inside the circle.

The area of a circle

= Πr²

where r is the radius of the circle.

Length of an arc of a circle

$length of an arc of a circle$

The length L of an arc of a circle is:

360

2Πr

where θ is the angle (in degrees) and r is the radius.

Area of an arc of a circle

$area of an arc$

The area A of an arc of a circle is:

360

Πr²

where θ is the angle (in degrees) and r is the radius.

Triangle along a semicircle

$triangle inside a semicircle$

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

$angles in a quadrilateral$

Angles in a quadrilateral add up to 360°

a + b + c + d = 360°

Angles in a rectangle

$angles in a rectangle$

Angles in a rectangle are all right angles (equal to 90°).

Area and Perimeter of a rectangle

$rectangle labelled$

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

$angles in a parallelogram$

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

$area of a parallelogram$

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

$equilateral triangle angles$

Angle: 60°

Interior angles add up to 180°

Square

$square angles$

Angle: 90°

Interior angles add up to 360°

Pentagon

$2d shapes pentagon angles$

Angle: 108°

Interior angles add up to 540°

Hexagon

$shapes for kids hexagon$

Angle: 120°

Interior angles add up to 720°

Heptagon

$heptagon angles$

Angle: 128.6° (to 1dp)

Interior angles add up to 900°

Octagon

$2d shape octagon$

Angle: 135°

Interior angles add up to 1080°

Nonagon

$2 dimensional shapes nonagon$

Angle: 140°

Interior angles add up to 1260°

Decagon

$decagon angles$

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

Geometry Formula Sheet - 3D Shapes

Cubes

$3 d shapes cube$

Volume of a cube:

= a x a x a = a³

where a is the length of each side.

Cuboid

$3d geometric shapes cuboid$

Volume of a cuboid

= length x width x height = lwh

Sphere

$3 dimensional shape sphere$

Volume of a sphere

4Πr³

where r is the radius of the sphere.

Cylinder

$geometry formula sheet cylinder$

Volume of a cylinder

= Πr²h

where r is the radius of the cylinder.

Cone

$geometry formula sheet cone$

Volume of a cone

Πr²h

where r is the radius of the widest part of the cone, and h is the height of the cone.

Square-based Pyramid

$square based pyramid volume$

Volume of a square based pyramid

b² x h

where b is the length of one side of the base, and h is the height of the pyramid.

Pyramid

$volume of a pyramid$

Volume of a pyramid

= ¹⁄₃ (area of base 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.

List of Geometric Shapes

Here you will find a List of different Geometric Shapes.

Included in this page are the following shapes:

triangles
quadrilaterals
regular and irregular polygons
a range of 3d shapes

Along with each of the shapes, some of the most important properties have also been included.

List of Geometric Shapes

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