,  ,     -  sides of a triangle

- semiperimeter

Heron's formula for calculating the Area of a triangle if given all sides ( A ) :

-  semi-major axis

-  semi-minor axis

3,14

Formula for calculating Area of an ellipse if given semi-major and semi-minor axes ( A ) :

- height  measured at right angles to the base

- equal sides

Calculate the Area of an equilateral triangle if given side or height ( A ) :

,  ,     -  sides of a scalene triangle

,  ,     -  angles

Calculate the Area of a triangle if given two sides and the included angle ( A ) :

,  ,     -  sides of a scalene triangle

,  ,     -  angles

Calculate the Area of a triangle if given two angles and a side ( A ) :

`1.  The area of a rhombus if you know diagonals and angle  `

-  larger diagonal

-  smaller diagonal

-  acute angle

-  obtuse angle

Calculate the Area of a rhombus if given diagonals and angle ( A ) :

`2.  The area of a rhombus if you know side and angle`

- side

,  -  angles

Calculate the Area of a rhombus when sides and angle are given ( A ) :

`3.  The area of a rhombus if you know side and radius of the inscribed circle  `

- side

- height

- radius  of the inscribed circle

Calculate the Area of a rhombus if given side and radius of the inscribed circle ( A ) :

`1.  The area of a parallelogram if you know sides and angle`

,  -  sides

,  -  angles

Formula for the area of a parallelogram when side and angle are given ( A ) :

`2.  How to find the area of a parallelogram if you know side(base) and height`

,  -  sides - base

- height  measured at right angles to the side

- height  measured at right angles to the side

Formula for the Area of a parallelogram if given side and height ( A ) :

`3.  The area of a parallelogram if you know diagonals and angle between them  `

,    -  diagonals

,  -  angles between the diagonals

Formula for the Area of a parallelogram with diagonals and angle between them ( A ) :

- length  of a rectangle

- width  of a rectangle

Calculate the Area of a rectangle if given length and width ( A ) :

- side

- diagonal

Calculate the Area of a square if given side (A) :

Calculate the Area of a square if given diagonal (A) :

`1.  How to find the area of a trapezoid (called a trapezium in the UK) if you know bases, height and middle line of a trapezoid  `

,

-  area of a trapezoid

Formula for area of a trapezoid if given bases, height and middle line. As well as you can use the calculator for calculating area. ( A ) :

`2.  How to find the area of a trapezoid (trapezium UK) if you know diagonals and angle between them`

,

,  -  angles between the diagonals

-  area of a trapezoid

Formula for area of a trapezoid if given diagonals and angle between them. As well as you can use the calculator for calculating area ( A ) :

`3.  How to find the area of a trapezoid (trapezium UK) if you know all sides  `

,  ,  ,

-  area of a trapezoid

Formula for area of a trapezoid if given all four sides. As well as you can use the calculator for calculating area ( A ) :

`Definition of a trapezoid (also known as trapezium)  `

Trapezoid is a quadrilateral in which only one pair of opposite sides are parallel

`Properties of a trapezoid (trapezium UK)  `

1. The middle line of the trapezoid is parallel to the bases and is equal to their half-sum.

2. The bisector of any angle of the trapezoid cuts off on its base (or continuation) an interval equal to the leg.

3. The triangles , formed by segments of the diagonals and the bases of the trapezoid, are similar.

4. Triangles formed by segments of the diagonals and the leg of the trapezoid, have the same area.

5. A circle can be inscribed into a trapezoid if the sum of the bases of the trapezoid is equal to the sum of its lateral sides.

6. The segment connecting the midpoints of the diagonals is equal to the half-difference of the bases and lies on the midline.

7. The intersection point of the diagonals of the trapezoid, the point of intersection of the extensions of its lateral sides and the middle of the bases lie on one straight line.

8. If the sum of the angles at any base of the trapezoid is 90 °, then the segment connecting the midpoints of the bases is equal to their half-difference.

`1.  The area of an isosceles trapezoid if you know sides and angle  `

-  lower base

-  upper base

-  equal lateral sides

- angle  at the lower base

Formula for calculating Area of a trapezoid if given all sides ( A ) :

Formulas for calculating Area of a trapezoid if given sides and angle ( A ) :

`2.  The area of an isosceles trapezoid in the case of a circle being inscribed in it  `

,      -  bases of an isosceles trapezoid

,       -  angles of an isosceles trapezoid

- radius  of the inscribed circle

- diameter  of the inscribed circle

- center  of the inscribed circle

Formulas  for calculating Area of a trapezoid if given radius, diameter or bases ( A ) :

For the circle inscribed into an isosceles trapezoid, the following is TRUE:

`3.  The area of an isosceles trapezoid in the case of a circle being inscribed in it and if you know middle line  `

,      -  bases of an isosceles trapezoid

-  equal lateral sides

- radius  of the inscribed circle

- center  of the inscribed circle

Formulas  for calculating Area of a trapezoid if given radius, sides or middle line ( A ) :

For the circle inscribed into an isosceles trapezoid, the following is TRUE:

`4.  The area of a isosceles trapezoid if you know diagonals and angle between them`

-  diagonal of a trapezoid

,  -  angles between the diagonals

Formula for calculating Area of a isosceles trapezoid if given diagonals and angle between them ( A ) :

`5.  The area of an isosceles trapezoid if you know lateral side, middle line and angle  `

-  equal lateral sides

- middle line

,  - angles at the bases

Formula for calculating Area of a trapezoid if given lateral side, middle line and angle ( A ) :

`6.  The area of an isosceles trapezoid if you know bases and height  `

,      -  bases of an isosceles trapezoid

- height  measured at right angles to the base

Formula for calculating Area of a trapezoid if given bases and height ( A ) :

-  side

-  number  of sides

Calculate the Area of a regular polygon if given side and number of sides   ( A ) :

-  diameter

3,14

Calculate the Area of a circle if given radius or diameter ( A ) :

-  length of the arc    AB

-  angle of the sector AOB

3,14

Calculate the Area of sector of circle if given length of arc ( A ) :

Calculate the Area of sector of circle if given central angle in degrees ( A ) :

-  angle of the segment

3,14

Calculate the Area of segment of circle if given radius and central angle in degrees ( A ) :

-  radius of the outer circle

-  radius of the inner circle

3,14

Calculate the Area of an annulus if given radii of the circles ( A ) :

-  radius of the outer circle

-  radius of the inner circle

-  angle of the sector AOB

3,14

Calculate the Area of a sector of an annulus if given radii of the circles and central angle in degrees ( A ) :

,    -  legs of a right triangle

Calculate the Area of a right triangle if given legs ( A ) :

- height  measured at right angle to the base

- base

Find the Area of a triangle if given height and base ( A ) :

- base  of an isosceles triangle

- height  measured at right angles to the base

- equal sides

Calculate the Area of an isosceles triangle if given sides or height and base ( A ) :