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Leg of a Trapezoid

Leg of a Trapezoid

Either of the two sides which connect the bases of a trapezoid.

 

Trapezoid with two parallel horizontal sides labeled "base" and two angled sides labeled "leg" connecting them.

Worked Example

Problem: A trapezoid has bases of length 10 and 4, and a height of 6. One leg is perpendicular to the bases (forming a right trapezoid). Find the length of the other leg.
Step 1: Sketch the trapezoid. Place the longer base (10) along the bottom. The shorter base (4) sits on top. One leg is vertical (perpendicular to the bases) with length 6, which equals the height.
Step 2: Find the horizontal distance the other leg must span. The top base is 4 and the bottom base is 10, so the horizontal gap on the non-vertical side is:
10−4=610 - 4 = 6
Step 3: The other leg is the hypotenuse of a right triangle with vertical side 6 (the height) and horizontal side 6. Apply the Pythagorean theorem:
ℓ=62+62=36+36=72=62\ell = \sqrt{6^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2}
Answer: The vertical leg has length 6, and the slanted leg has length 62≈8.496\sqrt{2} \approx 8.49.

Another Example

Problem: An isosceles trapezoid has bases of length 14 and 8, and each leg has length 5. Find the height of the trapezoid.
Step 1: In an isosceles trapezoid, both legs are equal. Drop perpendiculars from each end of the shorter base to the longer base. This creates two right triangles, one on each side.
Step 2: Find the horizontal base of each right triangle. The difference in the base lengths is split equally between the two sides:
14−82=3\frac{14 - 8}{2} = 3
Step 3: Each leg (length 5) is the hypotenuse of a right triangle with base 3. Solve for the height:
h=52−32=25−9=16=4h = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4
Answer: The height of the trapezoid is 4.

Frequently Asked Questions

How many legs does a trapezoid have?
A trapezoid always has exactly two legs. These are the two non-parallel sides. The other two sides are called the bases (the parallel pair).
What is the difference between a leg and a base of a trapezoid?
The two bases of a trapezoid are the sides that are parallel to each other. The two legs are the remaining sides that are not parallel — they connect one base to the other. In an isosceles trapezoid the legs are equal in length, but in a general trapezoid they can differ.

Leg of a Trapezoid vs. Base of a Trapezoid

The two bases are the parallel sides, while the two legs are the non-parallel sides that connect the bases. A trapezoid always has exactly two of each.

Why It Matters

Identifying the legs correctly is essential for computing a trapezoid's area, perimeter, and height. Many geometry problems require you to form a right triangle using a leg and the height, then apply the Pythagorean theorem. In coordinate geometry and real-world applications like bridge supports and table designs, the legs determine the slope and stability of the trapezoidal shape.

Common Mistakes

Mistake: Confusing a leg with a base, especially when a trapezoid is rotated so the parallel sides are not horizontal.
Correction: Always identify the two parallel sides first — those are the bases. The remaining two sides are the legs, regardless of the trapezoid's orientation.
Mistake: Assuming the two legs of a trapezoid are always equal in length.
Correction: Legs are equal only in an isosceles trapezoid. In a general or right trapezoid, the legs can have different lengths.

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