# Find the lengths of the parallel sides of a trapezium (US: trapezoid)

by Oshi

(Dubai)

**Question**

ABCD is a trapezium (US: trapezoid) of area 91cm

^{2}. CD is parallel to AB and CD is longer than AB by 8cm. if the distance between AB and CD is 7cm, find the lengths of AB and CD.

**Answer**

**STEP 1: **We know that, the area is 91cm

^{2} and CD is longer than AB. If we let AB be

*x*, CD is will be

*x+8*. Hence, we will have:

**STEP 2:** Now, since the distance between AB and CD is 7cm, the height of the trapezium is 7cm. Hence:

**STEP 3: **To find the lengths of AB and CD, we need to find

*x*. To do so, we start with the formula for the

area of a trapezium:

Where

*a* and

*b* are the parallel sides of the trapezium and

*h* is its height.

**STEP 4: **So, to find

*x*, we substitute

**a** with

*x*,

**b** with

*x+8*,

**h** with

*7* and

*A* with

**91**. This gives:

**STEP 5: **Now, we simplify the equation:

**STEP 6: **Notice that, to find

*x*, we need to remove 7. We can do so by dividing both sides of the equation with

**7**.

**STEP 7:** Now, we can find

*x* by adding

**-4** to both sides of the equation.

**STEP 8:** With

**x=9**, we can easily find the lengths of AB and CD: