Using the information in the following figure, find the area of the trapezium.

Draw a perpendicular line CP on AB, such that CP = 9 m and AP = 23 m.

Let PB = a m

In Δ CPB, by using the Pythagoras theorem,

Base² + Height² = Hypotenuse²

⇒ a² + (9)² = (15)²

⇒ a² + 81 = 225

⇒ a² = 225 - 81

⇒ a² = 144

⇒ a² = 144

⇒ a = $\sqrt{144}$

⇒ a = 12 m

So, AB = AP + PB = 23 + 12 = 35 m

Area of trapezium = $\dfrac{1}{2}$ (sum of parallel sides) x height

= $\dfrac{1}{2}$ (23 + 35) x 9

= $\dfrac{1}{2}$ x 58 x 9

= 29 x 9

= 261 m²

Hence, the area of the trapezium is 261 m².