Plane Geometry formula

Quadrilaterals

Area of Rectangle

A=ab

Perimeter of Rectangle

P=2(a+b)

Diagonal of a rectangle

Diagonal of a rectangle: d = √(a² + b²)

Area of square

A = a^2

Perimeter of Square

P=4a

Rectangle Inscribed in a square

General Quadrilaterals

Given diagonals and included angle

A=1/2 d1 d2 sin Θ

General Quadrilaterals

Given 4 sides and sum of opposite angles

A=√(s-a)(s-b)(s-c)(s-d)-abcdcos^2 Θ

s= ( a + b + c + d )/2

Θ = ( ∠A + ∠C)/2

Θ = (∠B + ∠D)/2

General Quadrilaterals

Given 4 sides and 2 opposite angles B and D

A= 1/2 ab sin B + 1/2 cd sin D

Parallelogram

Given Diagonal d1 and d2 and included angle

A=1/2 d1 d2 sin Θ

Parallelogram

Given 2 sides a and b and one angle A

A= ab sin A

Rhombus

Given d1 and d2

A=1/2 d1d2

Rhombus

Given side a and angle A

A=a^2sinA

Trapezoid Area

A=h/2 (a + b)

Trapezoid length of dividing line parallel to the two parallel side of a trapezoid

c=√ma^2+nb^2/m+n

m/m = A1/A2

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Cyclic Quadrilateral

Area

A=√(s-a)(s-b)(s-c)(s-d)

s = a + b + c + d /2

∠A + ∠C = 180

∠B + ∠D = 180

Ptolemy’s Theorem

d1d2=ac+bd