
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
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