Perimeter of a Trapezium

 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