

Area Formulas for Geometric Figures.
Area of a geometric figure is the number of square units that can fit inside a shape. Square units can be square inches (in^{2}),square feet (ft^{2}), square meters (m^{2}), etc.
Area of a triangle formulas
Area of a triangle when we know the base and the height
The area of a triangle is equal to half of base times height.
Area of a triangle when we know the lengths of all three of its sides (Heron's formula)
A = √s(s  a)(s  b)(s  c)
Area of a triangle when we know two sides and the included angle
The area of a triangle is equal to half of a product of two sides and sine of the angle between this sides.
Area of a triangle when we know three sides and circumradius
Area of a triangle when we know semiperimeter and inradius
The area of a triangle is equal to semiperimeter times inradius.
where A  the area of a triangle,
a, b, c  the length of sides BC,AC,AB accordingly,
h  the height, the length of the altitude,
α, β, γ  the angles,
r  the length of the inradius,
R  the length of the circumradius,
s =  a + b + c   the semiperimeter, or half of the triangle's perimeter.  2 
Area of a square formulas
Area of a square when we know the length of a side
The area of a square is equal to squared side.
A = a^{2}
Area of a square when we know the length of diagonal
The area of a square is half of squared diagonal.
where A  the area of a square,
a  the lenth of side,
d  the length of diagonal.
Area of a rectangle formula
The area of a rectangle is equal to a product of lenghts of two sides (height and width)
A = a · b
where A  the area of a rectangle,
a, b  the length of sides(the height and width of rectangle).
Area of a parallelogram formulas
Area of a parallelogram when we know the side and the height
The area of a parallelogram is equal to side times height.
A = a · h
Area of a parallelogram when we know two sides and the included angle
The area of a parallelogram is equal to a product of two sides and sine of the angle between this sides.
A = a · b · sin α
where A  the area of a parallelogram,
a, b  lengths of sides,
h  the height, the length of the altitude,
α  the measure of the angle between sides.
Area of a rhombus formulas
Area of a rhombus when we know the side and the height
The area of a rhombus is equal to side times height.
A = a · h
Area of a rhombus when we know length of a side and the included angle
The area of a rhombus is equal to a product of the squared side and sine of the angle between sides of a rhombus.
A = a^{2} · sin α
Area of a rhombus when we know length of its diagonals
The area of a rhombus is equal to half a product of it diagonals lengths.
where A  the area of a rhombus,
a  the length of a side,
h  the height, the length of the altitude,
α  the measure of the angle between sides of a rhombus,
d_{1}, d_{2}  the length of diagonals.
Area of a trapezium formulas
Heron's formula for a trapezium
A =  a + b  √(s  a)(s  b)(s  a  c)(s  a  d)  4a  b 
Area of a trapezium when we know length of 2 bases and the height
The area of a trapezium is equal to product of the height and halfsum of two bases
where A  the area of a trapezium,
a, b  the length of the 2 bases,i.e., the parallel sides,
c, d  length of the legs (the lateral sides),
s =  a + b + c + d   the semiperimeter, or half of the trapezium's perimeter.  2 
Area of a quadrangle formulas
Area of a quadrangle when we know length of its diagonals and angle between diagonals
The area of a quadrangle is equal to product of its diagonals and and sine of the angle between diagonals
where A  the area of a quadrangle,
d_{1}, d_{2}  the length of diagonals,
α  the angle between diagonals.
Area of a quadrangle when we know length of its perimeter and inradius
The area of a quadrangle is equal to perimeter timesinradius
A = p · r

Area of a quadrangle when we know length of its sides and value of opposite corners
A = √(s  a)(s  b)(s  c)(s  d)  abcd cos^{2}θ
where A the area of a quadrangle,
a, b, c, d  the length of sides,
s =  a + b + c + d   semiperimeter of quadrangle,  2 
θ =  α + β   half the sum of two opposite angles of a quadrilateral.  2 
Area of a rhombus circle
Area of a circle when we know its radius
The area of a circle is equal to a product of squared radius and pi.
A = π r^{2}
Area of a circle when we know its diameter
The area of a circle is equal to a quarter product of squared diameter and pi.
where A  the area of a circle,
r  the length of the radius,
d  the length of the diameter.
Area of a ellipse formulas
The area of an ellipse is equal to a product of lengths of the major and minor semiaxes and pi.
A = π · a · b
where A  the area of an ellipse,
a  the length of the major semiaxis,
b  the length of the minor semiaxis,
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