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Level 130

Polygons Theorems, Equations


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Euler's Formula
F+V=E+2 or F+V-2=E
Interior Angles Theorem
The sum of the inside angles of a convex polygon with n sides is 180(n-2).
Exterior Angles Theorem
The sum of the outside angles of a polygon is always 360 degrees.
Area of an N-gon
You can find the area by dividing it into triangles; A=(Area of one triangle)Number of trangles
S=2B+Ph=aP+Ph
Surface Area of a Right Prism
S=B+1/2Pl
Surface Area of a Regular Pyramid
S=πr2+πrl
Surface Area of a Right Cone
S=4πr2
Surface Area of a Sphere
S=2(πr2)+2πr(h)
Surface Area of a Cylinder
V=1/3Bh
Pyramid: Volume
V=Bh=πr2h
Volume of a Cylinder
V=1/3Bh=1/3πr2h
Volume of a Cone
V=(4/3)πr3
Volume of a Sphere
Scale Factor/Surface Area Theorem
If two similar solids have a scale factor of a:b, then corresponding areas of a ratio of a2:b2.
Surface Area/Volume Theorem
If two similar solids have a scale factor a:b, then corresponding volumes have a ratio of a3:b3.