The key property the a trapezium (as known in good Britain) or trapezoid (as known in the unified States) is the it is a 4 side shape with exactly one pair the parallel sides.

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.


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Example

Work the end the area of this trapezium.


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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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