How to find the area of the parallelogram?
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.
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.
I hope that these examples will help you in solving problems.