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Here's some though:

Area of a square:

A = s²

where s is the length of one side

Area of a rectangle:

A = lw

where 'l' is the length and 'w' is the width

Area of a triangle:

A = 1/2 bh

where b is the length of the base and h is the length of the altitude or the height

Area of a regular polygon:

where β=360/n

n is the number of sides, r is the radius of the circumscribing circle,

a is the length of one side of the polygon, h is the altitude or the height

Area of a circle:

A =π r² or

where r is the radius, d is the diameter

Area of a Cyclic Quadrilateral:

where s is the semiperimeter or half of the total perimeter

and a,b,c and d are the length of the sides of quadrilateral