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## Answers

Perimeter formula

Square 4 × side

Rectangle 2 × (length + width)

Parallelogram 2 × (side1 + side2)

Triangle side1 + side2 + side3

Regular n-polygon n × side

Trapezoid height × (base1 + base2) / 2

Trapezoid base1 + base2 + height × [csc(theta1) + csc(theta2)]

Circle 2 × pi × radius

Ellipse 4 × radius1 × E(k,pi/2)

E(k,pi/2) is the Complete Elliptic Integral of the Second Kind

k = (1/radius1) × sqrt(radius12 - radius22)

Area formula

Square side2

Rectangle length × width

Parallelogram base × height

Triangle base × height / 2

Regular n-polygon (1/4) × n × side2 × cot(pi/n)

Trapezoid height × (base1 + base2) / 2

Circle pi × radius2

Ellipse pi × radius1 × radius2

Cube (surface) 6 × side2

Sphere (surface) 4 × pi × radius2

Cylinder (surface of side) perimeter of circle × height

2 × pi × radius × height

Cylinder (whole surface) Areas of top and bottom circles + Area of the side

2(pi × radius2) + 2 × pi × radius × height

Cone (surface) pi × radius × side

Torus (surface) pi2 × (radius22 - radius12)

Volume formula

Cube side3

Rectangular Prism side1 × side2 × side3

Sphere (4/3) × pi × radius3

Ellipsoid (4/3) × pi × radius1 × radius2 × radius3

Cylinder pi × radius2 × height

Cone (1/3) × pi × radius2 × height

Pyramid (1/3) × (base area) × height

Torus (1/4) × pi2 × (r1 + r2) × (r1 - r2)2

Cube side3

Rectangular Prism side1 × side2 × side3

Sphere (4/3) × pi × radius3

Ellipsoid (4/3) × pi × radius1 × radius2 × radius3

Cylinder pi × radius2 × height

Cone (1/3) × pi × radius2 × height

Pyramid (1/3) × (base area) × height

Torus (1/4) × pi2 × (r1 + r2) × (r1 - r2)2