Isosceles Trapezoid Calculator
Calculate area, perimeter, height, diagonal, and angles of an isosceles trapezoid.
Trapezoid Dimensions
Both legs are equal
Results:
Area: 0.00 sq units
Perimeter: 0.00 units
Height: 0.0000 units
Diagonal: 0.0000 units
Base Angle: 0.00°
Top Angle: 180.00°
Step-by-Step Solution:
About Isosceles Trapezoids
What is an Isosceles Trapezoid?
An isosceles trapezoid is a trapezoid where the non-parallel sides (legs) are equal in length. It has one line of symmetry through the midpoints of the parallel sides.
Key Properties
- Both legs are equal in length
- Base angles are equal
- Diagonals are equal in length
- Has one line of symmetry
- Opposite angles are supplementary (sum to 180°)
Formulas
Height: h = √(c² - ((a-b)/2)²)
Area: A = ½(a + b)h
Perimeter: P = a + b + 2c
Diagonal: d = √(h² + (b + (a-b)/2)²)
Real-World Applications
- Architecture: Window frames, arch supports
- Furniture: Table bases, chair backs
- Engineering: Retaining walls, dam faces
- Design: Symmetric logos and patterns
Frequently Asked Questions
What makes a trapezoid isosceles?
A trapezoid is isosceles when both non-parallel sides (legs) have equal length. This creates symmetry and ensures that base angles are equal.
Are the diagonals equal in an isosceles trapezoid?
Yes! Unlike general trapezoids, an isosceles trapezoid always has equal diagonals. This is one of its defining characteristics.
How do I find the height?
Use the Pythagorean theorem: h = √(leg² - ((base₁ - base₂)/2)²). The height forms a right triangle with the leg and half the base difference.
What are the angle relationships?
Base angles on the same base are equal. Angles on opposite bases are supplementary (sum to 180°). If you know one angle, you can find all others.
Does an isosceles trapezoid have symmetry?
Yes, it has one line of symmetry that passes through the midpoints of both parallel bases, perpendicular to them. It does not have rotational symmetry.
Can all trapezoids be isosceles?
No, only trapezoids with equal leg lengths are isosceles. Most trapezoids have unequal legs and therefore are not isosceles.