https://file.aiquickdraw.com/mathbot/file/172946613307386thxn0z.jpg

To calculate the area of a trapezium, we use the formula:

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

where:
- \( a \) and \( b \) are the lengths of the two parallel sides,
- \( h \) is the height of the trapezium (the perpendicular distance between the parallel sides).

From the image:
- \( a = 19 \, \text{cm} \),
- \( b = 16 \, \text{cm} \),
- \( h = 10 \, \text{cm} \).

Now, we substitute the values into the formula:

\[
\text{Area} = \frac{1}{2} \times (19 + 16) \times 10
\]

\[
\text{Area} = \frac{1}{2} \times 35 \times 10 = 175 \, \text{cm}^2
\]

So, the area of the trapezium is **175 cm²**.

Would you like more details or have any questions?

Here are 5 related questions for further understanding:
1. How do you calculate the area of a trapezium with non-perpendicular sides?
2. Can the height of a trapezium always be drawn outside its shape?
3. What would happen to the area if the height was doubled?
4. How do you determine the height if only the side lengths are given?
5. How would you calculate the perimeter of this trapezium?

**Tip:** Remember that the height of a trapezium must always be the perpendicular distance between the parallel sides, even if drawn outside the shape.

Work out the area of the trapezium below.

Learn how to calculate the area of a trapezium with side lengths 19 cm, 16 cm, and a height of 10 cm. This problem is ideal for students in Grades 7-9, covering key geometric concepts such as the trapezium area formula.

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