# How to find the area of a quadrilateral?

Let's start with the definition of "quadrilateral". This is a figure consisting of four points and four segments, which connect all these points in pairs. It is important that no three of these points lie on the same line, since in this case, the quad is out. Points are called vertices of a quadrilateral, and segments are sides.

How to find the area of a quadrilateral? The formula for finding the area will depend on the type of quadrilateral. To solve this question, the formula is often used.S = d1 * d2 * sinβ / 2. Here d1, d2 are the diagonals of the quadrilateral (segments connecting the opposite vertices of the figure), β is the angle between them.

There are other formulas. Here is the table in which they are collected:

Special cases | ||

Name of quad | Elements used to calculate the area | Formula |

RECTANGLE | a, b - lengths of adjacent sides | S = a * b |

d is the length of the diagonal, β is the angle between the diagonals | S = d2* sinβ / 2 | |

SQUARE | a - side length | S = a2 |

d - diagonal length | S = d2/2 | |

PARALLELOGRAM | a - side length, ha - length of height, lowered to the side with length a | S = a * ha |

a, b are the lengths of adjacent sides, α is the angle between them | S = a * b * sinα | |

d1, d2 are diagonals, β is the angle between them | S = d1 * d2 * sinβ / 2 | |

RHOMBUS | a - side, ha - height, lowered to the side | S = a * ha |

a - side, α - angle between the sides (it is more convenient to choose a sharp angle, α "<" 90 = "" sup = ""> 0) | S = a2* sinα | |

d1, d2 - diagonal | S = d1 * d2 / 2 | |

KEYSTONE | a, b - lengths of bases, h - length of height, lowered to the base | S = (a + b) * h / 2 |

L is the length of the middle line, h is the length of the height lowered to the base | S = L * h | |

d1, d2 are diagonals, β is the angle between them | S = d1 * d2 * sinβ / 2 |

When solving the problem of finding the area of a quadrilateral, it is convenient to use the following algorithm:

- determine the type of the given quadrilateral
- highlight known items
- summarize the data under the formula

Now you know how to find the area of a quadrilateral.