Usually, a parallelogram consists of four sides. There are special parallelograms that have two congruent sides and two congruent diagonals. Still, the polygon must be a “quadrilateral” in geometry terms to be

considered a parallelogram for this article (if students read about another type of parallelogram, it has

to do with interior angles). Since there are four right angles in a parallelogram, all the exterior angles

equal one another. This is due to alternate interior angles being equal.

The area of a parallelogram is not any different than that of other quadrilaterals; it has the general

formula:

A = bh

A= area, b= base and h= height. However, it does depend on which side of the parallelogram is being

measured as to what formula will be used. The length of a diagonal in a parallelogram can be found

using trigonometry. Using trigonometry formulas for similar triangles, you get:

a^2 + b^2 = c^2

c^2 – a^2 = b^2

With these two equations, you have all of the trigonometric values needed to solve for one variable if

you know another value. In this case, one equation has 2 unknowns, so they must be solved together

using substitution. Once one has the value of c, you can plug it into the area formula to solve for area:

A = bc sin(θ)

Where θ is the angle between sides a and b, the angle will be given in the problem. Once one has found

this, one can derive another formula that gives that same result but measures length from the base

instead of height. This is done by flipping over both sides so that if A is the parallelogram then A would

switch to being bh, which gives one our other equation. This means that when measuring along the

base, C = 2a sin(θ). One can use either one of these formulas to solve for either height or base.

Properties of a parallelogram:

● Area is the same as other quadrilaterals (Pythagorean theorem).

● Alternate interior angles are equal (similarity of triangles).

● Exterior angles all equal each other (right angle triangle congruence postulate).

● Diagonals bisect each other.

● All four sides are congruent.

● Opposite angles are supplementary (180°).

● Consecutive angles form a linear pair, meaning they form straight lines with each other.

● If one knows one value for any side, they can derive the rest using trigonometry or just some

basic algebraic substitution.

● Parallelograms have two pairs of parallel sides and two pairs of congruent diagonals.

● One diagonal bisects the interior angle at its vertex and is drawn to opposite sides of the

parallelogram.

Uses of parallelogram:

● Used in many real-life applications, such as roofs or walls that support the weight of something.

● If one knows any two values, they can find all other angles and lengths. For example, if they

know the height and base length of a wall, you can find the angles because they are

supplementary.

● Can be used to represent many things, such as the sides of a room or even what triangles are in

real life.

A parallelogram is a complex figure (it has four sides and four right angles), which demands an

explanation of its parts–parallelogram name origin, parallelogram’s characteristics, the definition of

parallelogram, parallelogram properties, uses of a parallelogram.

A mathematical example for Parallelogram:

**Location:** A parallelogram can be found on a coordinate plane. The coordinates of the vertices are (-2,

4), (4, 3), and (6, 2). It is located under quadrant two.

**Shape**: The shape of a parallelogram is an exact square or rectangle. This is because all sides are

congruent, making them 90-degree angles.

**Area:** The area of a parallelogram will always be the same as any other shape because it is two

rectangles connected to form one figure. Therefore, its formula is bh, where h is the height and b is the

base. If one knows a side of the parallelogram, you can derive the rest by knowing one side and its

angle.

**Perimeter:** The perimeter of a parallelogram is 24 units because it consists of 4 right angles that each

have a length of 3, making them 9 units long.

A parallelogram is a very challenging concept. One can find more information for parallelograms on the

Cuemath website. It is an online platform that provides classes on math and coding to students in

various countries.