Shapes and area

GCSE Edecxel higher tier. based on the spec.

feel free to download but please leave a comment/ rating so I know whether it needs improving or not.

HideShow resource information
  • Created by: Alice
  • Created on: 03-06-11 10:25

Regular Polygons

equilateral triangle - 3 sides 3 lines of symmetry rotational symmetry order 3

square - 4 sides 4 lines rotational symmetry order 4

exterior angle = 360 degrees divided by the number of sides

interior angle = 180 - exterior angle

sum of exterior angles = 360

sum of interior angles = (n-2) x 180

the sum of angles works on any polygon not just regular ones.

nonagon - 9 sides

decagon - 10 sides

1 of 8


the line of symmetry is where you can fold the shape exactly in half. some shapes have more than one line of symmetry.

plane symmetry is to do with 3D objects. a plane mirror surface can be drawn through many regular solids but the shape must be exactly the same on both sides of the plane.          


rotational symmetry is where you can rotate a shape into different positions and it looks exactly the same.          

2 of 8


area of a triangle - half  x b x h or  half x a x b x sin(c)

area of a paralellogram - base x vertical height

area of a trapezuim - average of parralell sides x distance between them

area of a circle - pi x radius squared       circumference of circle - pi x diameter

area of a sector - ( length of arc - (

3 of 8

volumes - part 1

cubiod -

volume of cubiod = length x width x height

prism -

volume of prism = cross-sectional area x length

sphere -


4 of 8

volumes - part 2

pyramids and cones -

volume of pyramid = 1/3 x base area x height

volume of cone = (

a frustrum is a part of a cone; it is whats left when the top of a cone is cut off parallel to its circular base.

volume of frustrum = volume of original cone - volume of removed cone

5 of 8

simple geometry

angles in a triangle add up to 180

angles on a straight line add up to 180

angles in a quadrilateral add up to 360

angles round a point add up to 360

angles in a z shape are alternate angles

angles in a c and u shape are supplementary angles

angles in an f shape are corresponding angles

alternate angles; corresponding angles are equal

supplementary angles add up to 180

6 of 8

circle geometry checklist - make sure you can reco

angles in a semicircle = 90

tangent meets radius at 90

a chord bisector is a diameter

angles in the same segment are equal

angle at the centre is twice the angel at the edge

opposite angels of a cyclic quadrilateral add up to 180

angle in opposite segment are equal

equality of tangents from a point

sneaky isosclese triangles formed by two radii

7 of 8

the 4 transformations

the four transformations are : translation, englargement, rotation, reflection

translations are the ones with vectors and only the position of the object changes

englargements include scale factor and centre of englargement. you will need to identify these in order to get full marks on this question in the exam

refelctions involve a mirror line. these are pretty simple and easy to recognise

rotations are worth the most marks as you have to identify the most factors. you need to be able to identify the angle turned; the direction of rotation and the centre of rotation in order to gain full marks.

8 of 8



regular polygon page was really useful.thanks (:


this has helped me alot, i have been stressing out the past few days about this up-coming maths test, know i know i dont have to!<3


A good set of useful revision cards covering the basics of shape and their properties


Its okay to look at

Similar Mathematics resources:

See all Mathematics resources »See all Volume and surface area resources »