Quadrangles, polygons

Sides and diagonals of a parallelogram

$$2\cdot (a^{2}+b^{2}) = d1^{2}+d2^{2}$$

a, b - sides of a parallelogram
d1, d2 - diagonals of a parallelogram

Find It is known that:

Calculate 'a'

Sides and diagonals of a rhombus

$$d_{1}^{2}+d_{2}^{2} = 4\cdot a^{2}$$

a - side of a rhombus
d1, d2 - diagonals of a rhombus

Find It is known that:

Calculate 'd_1'

Diagonal of a square

$$d = a\cdot \sqrt {2}$$

Find It is known that:

Calculate 'd'

Trapezoid midline

$$m = \frac{a+b}{2}$$

a, b - bases of a trapezoid

Find It is known that:

Calculate 'm'

Height of an cyclic (inscribed ) antiparallelogram (isosceles trapezoid)

$$h = \sqrt {a\cdot b}$$

a, b - bases of a trapezoid

Find It is known that:

Calculate 'h'

The inradius of quadrilateral

$$r = \frac{S}{p}$$

r - the inradius of quadrilateral
S - area of a quadrilateral
p - half perimeter (semiperimeter) of a quadrilateral

Find It is known that:

Calculate 'r'

Angle of a regular polygon

$$\alpha = \frac{n-2}{n}\cdot 180$$

α - angle
n - number of angles or sides

Find It is known that:

Calculate 'α'

Sum of the angles of a polygon

$$s = (n-2)\cdot 180$$

n - number of angles or sides

Find It is known that:

Calculate 's'

Side of a regular polygon

$$a = 2\cdot R\cdot sin(\frac{180}{n})$$

n - number of angles or sides
R - circumradius

Find It is known that:

Calculate 'a'

Inradius of a regular polygon

$$r = R\cdot cos(\frac{180}{n})$$

r - inradius of a regular polygon
n - number of angles or sides
R - radius of circumcircle (circumradius)

Find It is known that:

Calculate 'r'

Circumradius of a square

$$R = \frac{a\cdot \sqrt {2}}{2}$$

a - side

Find It is known that:

Calculate 'R'

Inradius of a square

$$r = \frac{a}{2}$$

a - side

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Calculate 'r'

Circumradius of a regular hexagon

$$R = a$$

a - side

Find It is known that:

Calculate 'R'

Inradius of a regular hexagon

$$r = \frac{a\cdot \sqrt {3}}{2}$$

a - side

Find It is known that:

Calculate 'r'