Perimeter of Diagonal

The term "perimeter of diagonal" is not typically used in standard geometry; however, it can be understood as the total distance around a rectangle or square, including its diagonals.

For a rectangle, if you imagine walking along all four sides and its two diagonals, you would be covering the perimeter plus the diagonals.

The formula for the perimeter of a rectangle is 𝑃 = 2(𝑎 + 𝑏), where a and b are the lengths of the rectangle's sides.

The length of the diagonal d can be found using the formula 𝑑 = √(𝑎² + 𝑏²).

For instance, if a rectangle has sides a = 6 and b = 8, then its perimeter is p = 2(6 + 8) = 28, and the diagonal is d = √(6² + 8²) = 10.

Let’s consider another example of a rectangle with side lengths 𝑎 = 8 and 𝑏 = 10.

The perimeter of the rectangle will be 𝑃 = 2(𝑎 + 𝑏) = 2(8 + 10) = 36.

The diagonal length will be 𝑑 = √(8² + 10²) = √(64 + 100) = √164, approximately 12.81.

To find the perimeter including the diagonals of a rectangle, first calculate the perimeter of the rectangle using 𝑃 = 2(𝑎 + 𝑏). Then, add the length of the diagonal calculated using 𝑑 = √(𝑎² + 𝑏²).

For example, if a rectangle has sides of a = 6, b = 6, and you wish to include the diagonals, first find the perimeter = 2(6 + 6) = 24. Then, calculate the diagonal using 𝑑 = √(6² + 6²) = √72 ≈ 8.49.

Example Problem on Perimeter including Diagonals 

For finding the perimeter including the diagonal, use the formulas, 𝑃 = 2(𝑎 + 𝑏) and 𝑑 = √(𝑎² + 𝑏²). For example, let’s say, a = 5 cm, b = 4 cm.

Now, the perimeter = 2(5 + 4) = 18 cm, and the diagonal = √(5² + 4²) = √41 ≈ 6.4 cm.

Therefore, the total distance including the diagonal is 18 + 6.4 ≈ 24.4 cm.

Learning some tips and tricks makes it easier for children to calculate the perimeter including diagonals. Here are some tips and tricks given below:

• Always remember that the perimeter of a rectangle is simply 2 times the sum of the lengths of its two sides. For that, use the formula, 𝑃 = 2(𝑎 + 𝑏).

• Calculating the diagonal involves using the Pythagorean theorem where the diagonal acts as the hypotenuse. The formula is: 𝑑 = √(𝑎² + 𝑏²).

• To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of rectangles. After that, apply the formula to each shape.

• To avoid mistakes when adding the perimeter and diagonals, make sure the side lengths and diagonal lengths are precise for common uses like architecture and design. If you are given the diagonal and one side, you can use the Pythagorean theorem to find the other side.

• Perimeter: The total length of the sides of a shape.

• Diagonal: A line connecting two non-adjacent vertices in a polygon.

• Rectangle: A polygon with four sides and four right angles.

• Square: A polygon with four equal sides and four right angles.

• Pythagorean Theorem: A mathematical formula used to find the length of the sides in a right-angled triangle, often used to calculate diagonals.