Question

The area of an isosceles trapezium is 80 cm². If the parallel sides are 4 cm and 16 cm, find the (i) height and (ii) length of non-parallel sides.

Answer 1

Given:

• Area of isosceles trapezium = 80 cm²
• Lengths of parallel sides are 4 cm and 16 cm

Step 1: Find the height (h)

The area (A) of a trapezium is given by:

`A = 1/2 xx  "sum of parallel sides" xx h`

Substitute the given values:

`80 = 1/2 xx (4 + 16) xx h`

`80 = 1/2 xx 20 xx h`

`80 = 10 xx h`

`h = 80/10`

h = 8 cm

Step 2: Find the length of the non-parallel sides, the equal sides of the isosceles trapezium

Let the length of each non-parallel side be (x).

Since the trapezium is isosceles, the non-parallel sides are equal and the height forms a right triangle with half of the difference of the parallel sides and one of the non-parallel sides.

Calculate half of the difference of the parallel sides:

`(16 - 4)/2`

= `12/2`

= 6 cm

Use Pythagoras theorem for the right triangle formed by height (h), this half-segment 6 cm and the non-parallel side (x):

`x = sqrt(h^2 + 6^2)`

= `sqrt(8^2 + 6^2)`

= `sqrt(64 + 36)`

= `sqrt(100)`

= 10 cm

Height of trapezium = 8 cm

Length of non-parallel sides = 10 cm