Surface Area and Volume

• Polygon Interior Angles Theorem is the sum of the interior angles of a polygon= (n-2)180
• The formula for Regular Polygon Interior Angles is (n-2)180/n
• Polygon Exterior Angles Theorem says the exterior angles of a polygon equal 360 degrees
• The apothem is the distance from the center to the side of a polygon
• The area of a Regular N-gon is A=aP/2
• The area of an equilateral triangle is solved with A=(s²√3)/4
• To find the measure of a central angle use 360/n
• Euler's Theorem is F+V=E+2
• A solid is a 3d shape and a polyhedron
• A regular polyhedron has congruent faces, angles, and sides
• A convex polyhedron has (any) two points on its surface that can be connected by an inside segment
• A concave polyhedron has two points on its surface that when connected go outside the shape
• Polyhedron can't have curved edges and must be bound by polygons
• Surface area of prism formula is SA= 2B +Ph
• Surface area of cylinder is SA= 2B + Ch
• Surface area of pyramid is SA= B + Pl/2 (l is slant height)
• Surface area of cone is SA= B + Cl/2
• Volume is the number of CUBIC units in a solid
• Volume of a cube is V=s³
• Volume of a prism is V=bh
• Volume of a cylinder is V=πr^2h
• Volume of a pyramid is V=bh/3

  
• Volume of a cone is V=bh/3

  
• Volume of a sphere is V=4πr^3/3
• Surface area of a sphere is SA=4πr^2
• Similar Solids Theorem Area is corresponding areas have a ratio of a^2:b^2
• Similar Solids Theorem Volume is corresponding volumes have a ratio of a^3:b^3
• Displacement is finding the volume of an irregular object by subtracting one volume from another volume