Base of a Trapezoid

What Is the Base of a Trapezoid?

The base of a trapezoid refers to either of the two parallel sides of the shape.

A trapezoid has four sides in total:

• Two bases — the parallel sides (one on top, one on bottom)
• Two legs — the non-parallel sides (left and right)

The bases are always the two sides that run parallel to each other — meaning they never meet, no matter how far you extend them.

Top Base vs. Bottom Base

• The bottom base (b) is usually the longer parallel side at the bottom of the trapezoid
• The top base (a) is usually the shorter parallel side at the top

However, in math problems, either parallel side can be called “base 1” and “base 2” — the labeling does not change how you calculate anything.

Base vs. Leg — What Is the Difference?

Properties of the Bases of a Trapezoid

• A trapezoid always has exactly two bases
• The two bases are always parallel to each other
• The two bases are usually different lengths (except in a parallelogram, where they are equal)
• The height of a trapezoid is always measured perpendicularly (at 90°) between the two bases — never along the leg
• The midsegment of a trapezoid connects the midpoints of the two legs and is always equal to the average of the two bases: Midsegment = (a + b) / 2

How to Find the Base of a Trapezoid

You may need to find a missing base in two common situations:

Method 1 – Using the Area Formula

If you know the area and the height, you can find a missing base.

Formula: Area = (a + b) / 2 × h

Rearranged to find a missing base:

(a + b) = (2 × Area) / h

Then subtract the known base to find the missing one:

b = (2 × Area) / h − a

Method 2 – Using the Midsegment Formula

If you know the midsegment (m) and one base, you can find the other base.

Formula: m = (a + b) / 2

Rearranged: b = 2m − a

Solved Examples

Example 1 – Identifying the Bases

A trapezoid has sides of 6 cm, 10 cm, 5 cm, and 5 cm. The two parallel sides are 6 cm and 10 cm. What are the bases?

Solution:

• Top base (a) = 6 cm
• Bottom base (b) = 10 cm
• The two legs are each 5 cm (non-parallel sides)

Example 2 – Finding a Missing Base Using Area

The area of a trapezoid is 48 cm². The height is 6 cm and one base is 9 cm. Find the other base.

Solution:

b = (2 × Area) / h − a

b = (2 × 48) / 6 − 9

b = 96 / 6 − 9

b = 16 − 9

b = 7 cm

Example 3 – Finding a Missing Base Using the Midsegment

The midsegment of a trapezoid is 11 m and one base is 8 m. What is the other base?

Solution:

b = 2m − a

b = 2(11) − 8

b = 22 − 8

b = 14 m

Example 4 – Real-World Problem

A trapezoidal tabletop has an area of 90 in² and a height of 9 in. The front edge (bottom base) measures 14 in. What is the length of the back edge (top base)?

Solution:

a = (2 × 90) / 9 − 14

a = 180 / 9 − 14

a = 20 − 14

a = 6 in

Practice Questions

Try these on your own! Answers are listed below.

Question 1: A trapezoid has sides 5 cm, 11 cm, 4 cm, and 6 cm. The parallel sides are 5 cm and 11 cm. Identify the top and bottom base.

Question 2: The area of a trapezoid is 70 m², the height is 7 m, and one base is 8 m. Find the missing base.

Question 3: The midsegment of a trapezoid is 9 in and one base is 5 in. Find the other base.

Question 4: A trapezoid has an area of 100 cm², a height of 10 cm, and a bottom base of 15 cm. What is the top base?

Question 5: The two bases of a trapezoid are in a ratio of 1:3. The midsegment is 12 cm. Find both bases.

Answers:

1. Top base = 5 cm, Bottom base = 11 cm
2. 12 m
3. 13 in
4. 5 cm
5. 6 cm and 18 cm (a + b = 24, ratio 1:3 → a = 6, b = 18)

Frequently Asked Questions (FAQs)