# How to find the middle line of an isosceles trapezoid?

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It is customary to call a trapezium such a quadrilateral in which only two sides are parallel to each other. These sides are the bases of the trapezium. The other two sides are called the sides.

The trapezoid is called the isosceles one, in which the lengths of the lateral sides are equal to each other.

## Middle trapezium line

The middle line is the line that connects the middle of the two sides of the figure.

How to find the middle trapezoid line if the trapezoid is isosceles?

There are several ways.

## Methods for finding the midline of an isosceles trapezoid

### Method 1.

If we know the lengths of the bases of a trapezoid, then we use the formula:

- m = (a + b) / 2, where:
- m is the length of the midline
- a and b are base lengths

### Method 2.

If we know the length of the side, then we need additional information. There can be two cases:

#### Case A

We will have enough side length and perimeter of the trapezium.

- The formula: m = (P - 2 * c) / 2, where
- m is the middle line,
- P - perimeter
- s is the side.

#### Case B

In addition to the length of the side, it will be necessary to know the length of the height of the trapezoid and the length of one of the bases.

Formula:

- m = a is the root of (c2- h2)

or

- m = b + root of (c2- h2), where
- m - middle line
- a is a greater basis,
- b - smaller base
- s - side
- h - trapezium height

## Examples

Let's consider each case on specific examples. The task will be the same everywhere: find the middle line of an isosceles trapezoid.

### 1 way

Given: one base of an isosceles trapezoid is 4 cm, the second is 6 cm

- The solution is: m = (4 + 6) / 2 = 10/2 = 5
- Answer: 5 cm.

### 2 way, case A

Given: the side of an isosceles trapezoid is 3 cm, the perimeter is 20 cm.

- The solution is: m = (20 - 3 * 2) / 2 = (20 - 6) / 2 = 7
- Answer: 7 cm

### 2 way, case B

Given: the smaller of the bases of an isosceles trapezoid is 4 cm, the height of the trapezoid is 3 cm, and the side is 5 cm.

Decision:

Since the ground is given to us less, we choose the formula with the sign +

- m = 4 + root of (52-32) = 4+ the root of 16 = 4 + 4 = 8.