# How to find the area of a rectangle

The rectangle belongs to the simplest flat geometrical figures and is one of special cases of a parallelogram. Distinctive feature of such parallelogram - right angles in all four tops. The area limited to the parties of a rectangle can be calculated in several ways, using the sizes of its parties, diagonals and corners between them, the radius of an inscribed circle, etc.

## Instruction

1. If lengths of the parties of a rectangle are known (N and W), just multiply its height on width and the required area will be result: S= H*W.

2. If corner size (α) which makes rectangle diagonal from one of its parties and also length is known (C) this diagonal, then for calculation of the area it is possible to involve definitions of trigonometrical functions in a rectangular triangle. The rectangular triangle is formed here by two parties of a quadrangle and its diagonal. From definition of a cosine follows that length of one of the parties will be equal to the work of length of diagonal on a cosine of the angle which size is known. It is possible to bring a formula of length of other party out of definition of a sine - it is equal to the work of length of diagonal on a sine of the same corner. Substitute these identities in a formula from the previous step, and it will turn out that for finding of the area it is necessary to multiply a sine and a cosine of the known corner and also a rectangle diagonal length square: S=sin (α)*cos(α) * With².

3. If except diagonal length (C) a rectangle corner size is known (β) which is formed by diagonals, then it is possible to use for calculation of the area of a figure one of trigonometrical functions too - a sine. Square length of diagonal and increase the received result by a half of a sine of the known corner: S=C²*sin (β)/2.

4. If the radius (r) of the circle entered in a rectangle is known, then for calculation of the area build this size in the second degree and increase result four times: S=4*r². The quadrangle in which it is possible to enter a circle will be a square, and length of its party is equal to diameter of an inscribed circle, that is the doubled radius. The formula is received by substitution of lengths of the parties expressed through radius in identity from the first step.

5. If lengths of perimeter (P) and one of the parties (A) of a rectangle are known, then for finding of the area in this perimeter calculate a half of the work of length of the party on a difference between length of perimeter and two lengths of this party: S=A*(P-2*A)/2.

Author: «MirrorInfo» Dream Team