Area and Perimeter of Rectangle / Parallelogram Calculator

Area and Perimeter of Rectangle / Parallelogram Calculator

You can find the area and parameters for both rectangles and parallelograms with this calculator. It works as four in one tool.  

What are rectangles and parallelograms?

Rectangles and parallelograms are both quadrilaterals, which means they have four sides. They share the property that their opposite sides are equal in length, and their opposite angles are equal. 

This commonality arises from the fact that the rectangle is a special type of parallelogram, one where all angles are right angles (90 degrees).

However, while all rectangles are parallelograms, not all parallelograms are rectangles. A parallelogram only requires that its opposite sides are parallel and of equal length. The angles in a parallelogram do not have to be 90 degrees. If they are, then it is a rectangle.

The formula for the area:

Despite the differences in shape, the formulas for calculating the area of both a rectangle and a parallelogram are structurally similar. They both involve the multiplication of two quantities: base and height.

Rectangle: In a rectangle, you can take any two adjacent sides as base and height due to the right angles. The formula for the area (A) is A = base * height. Formerly it was A = length * width

Parallelogram: In a parallelogram, the base is any side, and the height is the perpendicular distance from this side (the base) to the opposite side. This could mean that the 'height' is not a side of the parallelogram. The formula for the area (A) is A = base * height.

Solved Examples:

Let's consider examples where a rectangle and a parallelogram have the same base and height.

Rectangle: Suppose we have a rectangle where the base is 5 units and the height is 7 units. Using the formula A = base * height, the area of the rectangle would be A = 5 * 7 = 35 square units.

Parallelogram: Now, consider a parallelogram with the same base of 5 units and a height of 7 units (imagine the height as a line inside the parallelogram drawn perpendicularly from the base to the opposite side). 

Using the formula A = base * height, the area of the parallelogram would be A = 5 * 7 = 35 square units, the same as the rectangle's area in this case.

The formula for the Perimeter:

The perimeter of a shape is the distance around its edge. In the case of rectangles and parallelograms, the formulas are the same.

Rectangle: The perimeter (P) of a rectangle is calculated by adding the lengths of all four sides. Because opposite sides of a rectangle are equal, this can also be calculated by doubling the sum of the length (L) and the width (W). The formula for the perimeter of a rectangle is: P = 2L + 2W

Parallelogram: The perimeter (P) of a parallelogram is also calculated by adding the lengths of all four sides. Since a parallelogram has equal opposite sides, this can be calculated by doubling the sum of the base (B) and the side length (S). The formula for the perimeter of a parallelogram is: P = 2B + 2S

Solved Examples:

Let's consider examples where a rectangle and a parallelogram have the same base and side lengths.

Rectangle: Imagine a rectangle where the length is 5 units and the width is 7 units. Using the formula P = 2L + 2W, the perimeter of the rectangle would be P = 25 + 27 = 10 + 14 = 24 units.

Parallelogram: Now, consider a parallelogram with the same base of 5 units and a side length of 7 units. Using the formula P = 2B + 2S, the perimeter of the parallelogram would be P = 25 + 27 = 10 + 14 = 24 units, the same as the rectangle's perimeter in this case.