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Lesson 7, Topic 6
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# Perimeter of a Trapezium

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A trapezium is a four-sided figure with one pair of parallel sides.

### Isosceles Trapezium

An isosceles trapezium has one pair of opposite sides parallel and the non-parallel sides are equal in length.

Perimeter  =   x  + y   +  x  +  z

= x  +  x   +  y  +   z

= 2x   +   y   +  z

### Example:

An isosceles trapezium has a perimeter of 48cm. If the sizes of the unequal parallel sides are 10cm and 6cm. Calculate the size of one of the equal sides.

Solution

Perimeter of a Trapezium = 2x   +   y   +  z

Perimeter =  48cm

x = ?
y = 10cm
z = 6cm

Substitute the values into the equation

48 = 2x + 6 + 10

48 = 2x + 16

move the unknown, x, to the left hand side

2x + 16 = 48

subtract both sides by 16

2x + 16 – 16 = 48 – 16

2x = 32

divide both sides by 2

$$\frac{2x}{2} = \frac{32}{2}$$

$$\frac{\not{2}x}{\not{2}} = \frac{32}{2}$$

x = $$\frac{32}{2}$$

x = 16 cm