Area of Parallelogram Questions (with Solutions)

2D or 3D shapes are the foundation of geometry. Each of these shapes has a unique set of features and uses a distinct area formula. The area of a parallelogram is the space it takes up on a two-dimensional plane. The area of a parallelogram is the region enclosed by its four sides. The area of a parallelogram is found by multiplying its length by its height.

What Is A Parallelogram?

A parallelogram is a four-sided, two-dimensional shape in geometry. It is a unique quadrilateral instance where the opposing sides are parallel and equal. The total of a quadrilateral's internal angles is 360 degrees. Two pairs of parallel sides with equal lengths make up a parallelogram. It has a perimeter and area because it is a two-dimensional figure. A parallelogram's interior opposite angles are also similar. A parallelogram has adjacent angles that sum to 180 degrees. Anything from a rectangle to a square to a rhombus can be a parallelogram.

What Is The Formula To Determine A Parallelogram's Area?

To find the parallelogram's area, multiply the perpendicular base by its height. In contrast to the lateral side of the parallelogram, which is not perpendicular to the base, the parallelogram's base and height are perpendicular to one another.

Therefore, the area of a parallelogram can be calculated using the formula below:

Area of parallelogram = Base * Height

If the length of adjacent sides and the angle between them are known, the area of a parallelogram can also be determined without knowing its height.

Area of parallelogram = ab\sin\theta

Here, ‘a’ and ‘b’ represents the length of parallel sides and \theta .

The length of a parallelogram's diagonals can also be used to determine its area. A parallelogram has two diagonals that cross one other at specific angles.

Area of parallelogram = \frac{1}{2}d_{1}d_{2}\sin x

Here, d_{1} and d_{2} represent the lengths of the two diagonals and ‘x’ represents the angle between the two diagonals.

Perimeter Of Parallelogram

Any shape's perimeter is either its entire length or the total distance enveloping it. In a similar manner, the total length of a parallelogram's edges determines its perimeter. Consequently, the following can be used to write the perimeter calculation formula:

Perimeter of parallelogram = 2(a+b)

Here, ‘a’ and ‘b’ represent the lengths of the sides of a parallelogram.

Types Of Parallelograms

There are three different types of parallelograms, as follows:

• Rhombus - A parallelogram with equal sides is a rhombus. Every rhombus is a parallelogram because every pair of opposite sides is parallel.

• Rectangle - A rectangle is a parallelogram when the diagonals are equal and all angles are right angles. Each interior angle of a rectangle, which is a particular instance of a parallelogram, is 90 degrees in measurement.

• Square - A parallelogram with all equal sides and all 90-degree angles is called a square. The diagonals of a square are also equal.

Properties Of Parallelogram

The characteristics of a parallelogram are as follows:

• Both sides will be congruent and parallel.

• Congruence exists between the opposite angles.

• The other angles are all right angles if any of the angles are right angles.

• The two diagonals will cut each other in half.

• The parallelogram is split into two congruent triangles by each diagonal.