You are watching: How many lines of symmetry in a trapezoid

Depending on exactly how the trapezium is attracted determines how plenty of lines of symmetry if has.

The trapezium in ~ the top has one vertical line of reflectional symmetry and also the trapezium at the bottom that the photo has no currently of symmetry.

A trapezium doesn’t have actually rotational symmetry so the bespeak of rotational the opposite is 1.

You deserve to work the end the area that a trapezium by using the formula A = ½(a+b)h. Where a and also b space the lengths that the parallel sides and h is the shortest distance in between the two parallel sides.

Example

Work the end the area of this trapezium.

The 2 parallel sides space 8cm and also 10cm. So a = 8 and also b = 10. The doesn’t matter if you have actually these the other way around.

The shortest distance in between the parallel sides is 6cm therefore h = 6.

All you have to do now is substitute these 3 values right into the formula:

A = ½(a+b)h

A = ½ (8+10)6

A = ½ × 18 × 6 = 54 cm²

Alternatively, due to the fact that the trapezium was symmetrical you could split up the trapezium right into 2 triangle and also a rectangle:

Area of each triangle = (6 × 1) ÷ 2 = 3cm²

Area of the rectangle = 8 × 6 = 48cm²

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

Working the end the area of a trapezium is a common question on most exam papers, and you have the right to use trapeziums to calculation the area enclosed in between a curve and also the coordinate axes (this is recognized as the trapezium rule).

So to summarise the nature of a trapezium:

a) A quadrilateral with a pair of parallel sides.

b) 0 or 1 lines of reflectional symmetry.

c) no rotational symmetry.

d) area that a trapezium A = ½(a+b)h.

## Questions & Answers

**Question:**What nature does a trapezium have?

**Answer:** A trapezium have the right to be attracted in different ways, for this reason the properties can vary, however it should have specifically one pair the parallel sides.

**Question:** What present of symmetry does an rarely often, rarely trapezium have?

**Answer:** the will have 0 present of reflectional symmetry.

**Question:** Is a rectangle a square?

**Answer:** No, a rectangle is not a square.

A square has actually 4 same side lengths, and also a recangle has actually 2 bag of same side lengths.

**Question:** How many lines go a trapezoid have?

**Answer:** A symmetrical trapezoid will have 1 line of symmetry.

If not then the prize is 0.

**Question:** What properties does a rhombus have?

**Answer:** A rhombus has 4 same side lengths.

The angles oppisite each various other are equal.

It has 2 currently of reflectional symmetry, and also order 2 rotational symmetry.

The diagonals that the rhombus bisect each various other at 90 degrees.

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