# Maths- shapes and area

Maths GCSE, part 2 of 6.

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• Created by: carys
• Created on: 02-06-12 16:13

## Regular polygons

Polygons- a multisided shape. A regular polygon is where all the sides and angles are the same.

Equilateral triangle- has 3 sides, 3 lines of symmetry and 3 rotations of symmetry

Regualar pentagon- 5 sides, 5 lines of symmetry and 5 rotations of symmetry

Exterior angles = 360/n

Interior angles = 180 - exterior angle

Sum of exterior angles = 360

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

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## Areas

Triangle- 1/2 x base x vertical height

Parallelogram- base x vertical height

Trapezium- average of parallel sides (1/2 x a + b) x distance between them (height)

Area of circle- Pi x (radius)2

Circumference of circle- Pi x diameter

Area of sector- angle size of sector divided by 360 x area of full circle

Length of arc- angle size of sector divided by 360 x circumference of full circle

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## Surface area and volumes

Surface area and volume- only occur for 3D shapes

Surface area of solid = area of net

Volume of cuboid = length x width x height

volume of prism = cross-sectional area x length

volume of sphere = 4/3 x pi x radious3

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

volume of cone = 1/3 x pi x radius3 x height

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