# How Many Lines Of Symmetry Does A Trapezoid Have

Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.

The main property of a trapezium (as known in Great Britain) or trapezoid (as known in the United States) is that it is a 4 side shape with exactly one pair of parallel sides. The way in which the trapezium is drawn determines how many lines of symmetry it has. The trapezium at the top has one vertical line of reflectional symmetry and the trapezium at the bottom of the picture has no lines of symmetry. A trapezium doesn’t have rotational symmetry so the order of rotational symmetry is 1.

You can work out the area of a trapezium by using the formula A = ½(a+b)h. Where a and b are the lengths of the parallel sides and h is the shortest distance between the two parallel sides.

The two parallel sides are 8cm and 10cm. So a = 8 and b = 10. It doesn’t matter if you have these the other way around.

Alternatively, since the trapezium was symmetrical you could split up the trapezium into 2 triangles and a rectangle:

So the total area of the trapezium is 48 + 3 + 3 = 54 cm²

Working out the area of a trapezium is a common question on most exam papers, and you can use trapeziums to estimate the area enclosed between a curve and the coordinate axes (this is known as the trapezium rule).

Answer: A trapezium can be drawn in different ways, so the properties can vary, but it must have exactly one pair of parallel sides.

A square has 4 equal side lengths, and a recangle has 2 pairs of equal side lengths.

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## Question:

How many lines of symmetry does a trapezoid have?

Symmetry is a word you may have come across in either art or math. When something is symmetrical, it is a mirror of itself. In math, we can draw lines of symmetry on polygons when the two sides are exactly the same. For example, a rectangle has two lines of symmetry because you can fold it over itself both horizontally and vertically, and it doesnt overlap.

## Trapezoid:

A trapezoid is a quadrilateral that consists at least one pair of parallel sides. Trapezoids have four sides.

The formula for the area of a trapezoid is:

{eq}A = frac{1}{2}(text{Sum of two parallel sides}) times (text{distance between two parallel sides}) {/eq}

In a trapezoid, opposite angles are equal and supplementary angles.

The two parallel sides are 8cm and 10cm. So a = 8 and b = 10. It doesn’t matter if you have these the other way around.

Working out the area of a trapezium is a common question on most exam papers, and you can use trapeziums to estimate the area enclosed between a curve and the coordinate axes (this is known as the trapezium rule).

Alternatively, since the trapezium was symmetrical you could split up the trapezium into 2 triangles and a rectangle:

A square has 4 equal side lengths, and a recangle has 2 pairs of equal side lengths.

You can work out the area of a trapezium by using the formula A = ½(a+b)h. Where a and b are the lengths of the parallel sides and h is the shortest distance between the two parallel sides.

## FAQ

Which shape has 4 lines of symmetry?

No a trapezoid can’t have two lines of symmetry because only one pair of parallel sides are equal in the case of a quadrilateral.

Can a trapezoid have 0 lines of symmetry?

Square. A square has four lines of symmetry.