Diagonal Calculator
Calculate diagonal length and number of diagonals for rectangles, squares, and polygons.
Dimensions
Results:
Number of Diagonals: 0
Step-by-Step Solution:
About Diagonals
What is a Diagonal?
A diagonal is a line segment connecting two non-adjacent vertices of a polygon. In quadrilaterals, diagonals connect opposite corners.
Diagonal Formulas
Rectangle: d = √(length² + width²)
Square: d = side × √2
Rhombus/Kite: Area = (d₁ × d₂) / 2
Number of Diagonals: n(n-3)/2 for n-sided polygon
Diagonal Properties
- Rectangle: Diagonals are equal and bisect each other
- Square: Diagonals are equal, perpendicular, and bisect each other at 90°
- Parallelogram: Diagonals bisect each other but are not equal
- Rhombus: Diagonals are perpendicular and bisect each other
- Trapezoid: Diagonals are not equal (except isosceles trapezoid)
Real-World Applications
- Construction: Ensuring rectangularity of structures
- TV/Monitor Size: Screens measured by diagonal length
- Carpentry: Checking square corners (3-4-5 rule)
- Engineering: Structural bracing and support
Frequently Asked Questions
How many diagonals does a quadrilateral have?
Every quadrilateral has exactly 2 diagonals. Using the formula n(n-3)/2 where n=4: 4(4-3)/2 = 2.
Why is the square diagonal side√2?
Using Pythagorean theorem: d² = s² + s² = 2s², so d = √(2s²) = s√2 ≈ 1.414s.
Are rectangle diagonals always equal?
Yes, both diagonals of a rectangle are always equal in length. This is one of the defining properties of rectangles.
How do you calculate diagonal from area?
For a rectangle, if you know the area and one dimension, find the other dimension first, then use the Pythagorean theorem to find the diagonal.
What polygon has the most diagonals?
The more sides a polygon has, the more diagonals it has. The formula n(n-3)/2 shows that diagonals increase quadratically with the number of sides.
Do triangle have diagonals?
No, triangles have no diagonals. Using the formula n(n-3)/2 where n=3: 3(3-3)/2 = 0.
How are TV screens measured?
TV and monitor sizes are measured diagonally from corner to corner. A "55-inch TV" has a 55-inch diagonal measurement.
What's the 3-4-5 rule for checking square corners?
If you measure 3 units on one side, 4 units on another, the diagonal should be 5 units if the corner is perfectly square (90°). This comes from the Pythagorean theorem: 3² + 4² = 5².