# How to find the area of a parallelogram

Parallelogram is a quadrilateral whose opposite sides are parallel (they are located in parallel lines). The parallelograms are differentiated by the size of the adjacent sides as well as by the angles, however, the opposite sides are equal. How to find the area of a parallelogram?

#### Some characteristics of the parallelogram

- A quadrilateral has two pairs of parallel sides:

AB||CD, BC||AD - A quadrilateral has a pair of parallel and equal sides:

AB||CD, AB = CD (или BC||AD, BC = AD) - In a quadrilateral the opposite sides are equal:

AB = CD, BC = AD - In a quadrilateral the opposite angles are equal:

∠DAB = ∠BCD, ∠ABC = ∠CDA - In a quadrilateral the diagonals are divided in half with the intersection point:

AO = OC, BO = OD - The sum of adjacent angles on either side is 180 °:

∠ABC + ∠BCD = ∠BCD + ∠CDA = ∠CDA + ∠DAB = ∠DAB + ∠DAB = 180° - In a quadrilateral the sum of squares of diagonals is equal to the sum of squares of their sides:

AC^{2}+ BD^{2}= AB^{2}+ BC^{2}+ CD^{2}+ AD^{2}

The square, the rectangle and the rhombus are parallelograms.

The diagonal of a parallelogram is any segment that joins two vertices of the opposite angles of a parallelogram.

### How to find the area of a parallelogram?Formula of the area of a parallelogram through two diagonals and the sine of the angle between them:

- The area of a parallelogram is a space limited by the sides of a parallelogram, that is, within the perimeter of a parallelogram. The perimeter of a parallelogram is the sum of the lengths of all sides of a parallelogram.

### The Formulas:

- Formula of the area of a parallelogram through the side and height related to this side:

A = a · h_{a}

A = b · h_{b } - Formula of the area of a parallelogram through two sides and the sine of the angle between them:

A = ab sinα

A = ab sinβ - Formula of the area of a parallelogram through two diagonals and the sine of the angle between them:

A = ½d_{1}d_{2}sin γ

A = ½d_{1}d_{2}sin δ

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