The area of a trapezium (trapezoid) can be found using the formula:

$\text{Area} = \frac{1}{2} \times (a + b) \times h$

Where:

• $a$ and $b$ are the lengths of the parallel sides,
• $h$ is the height,
• and the area is given.

Given:

• Area = 14300 cm²
• $a = 140$ cm
• $b = 80$ cm

We need to find the height $h$.

Plugging the values into the formula:

$14300 = \frac{1}{2} \times (140 + 80) \times h$

Simplifying:

$14300 = \frac{1}{2} \times 220 \times h$

$14300 = 110 \times h$

Now, solve for $h$:

$h = \frac{14300}{110} = 130 \, \text{cm}$

So, the height $h$ of the trapezium is 130 cm.

Would you like a further breakdown or more examples?

Here are 5 related questions:

1. What is the formula for finding the perimeter of a trapezium?
2. How would you calculate the area of a trapezium if only the height and one of the parallel sides were given?
3. What is the difference between a trapezium and a parallelogram?
4. How would changing one of the parallel sides affect the area of the trapezium?
5. Can you solve for the height if the area was given in meters instead of centimeters?

Tip: Always ensure that the units are consistent when performing area calculations to avoid errors!