# How to find the area of ​​the parallelogram?

Leonid Veselov
August 16, 2012
26998

Before we learn how to find the area of ​​a parallelogram, we need to remember what a parallelogram is and what is called its height. A parallelogram is a quadrilateral whose opposite sides are in pairs parallel (lie on parallel straight lines). A perpendicular drawn from an arbitrary point on the opposite side to a line containing this side is called the height of the parallelogram.

The square, the rectangle and the rhombus are special cases of the parallelogram.

The area of ​​the parallelogram is denoted by (S).

## Formulas for finding the area of ​​a parallelogram

S = a * hwhere a is the base, h is the height that is drawn to the base.

S = a * b * sinα, where a and b are bases, and α is the angle between the bases of a and b.

S = p * rwhere p is a semi-perimeter, r is the radius of the circle, which is inscribed in the parallelogram.

The area of ​​the parallelogram, which is formed by the vectors a and b, is equal to the modulus of the product of the specified vectors, namely:

S = | a x b |

Consider the example number 1: Given a parallelogram whose side is 7 cm and a height of 3 cm. How to find the area of ​​the parallelogram, the formula for the solution we need.

Decision:

S = a * h

Thus, S = 7x3. S = 21. Answer: 21 cm2.

Consider the example number 2: Given the base of 6 and 7 cm, and also given the angle between the bases of 60 degrees. How to find the area of ​​the parallelogram? The formula used to solve:

S = a * b * sinα

Thus, we first find the sine of the angle. Sine 60 = 0.5, respectively S = 6 * 7 * 0.5 = 21 Answer: 21 cm2.
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