Question 2

We will find the height of the trapezium first, then use it to calculate the area.

Step 1 — Find the base of the right triangle

We need to find the length of the base of the right-angled triangle formed.

Let's subtract the shorter parallel side from the longer one.

$= 40 \text{ cm} - 20 \text{ cm}$

$= 20 \text{ cm}$

Now, we divide this difference by 2 because the non-parallel sides are equal.

This gives us the base of each right-angled triangle.

$= \frac{20 \text{ cm}}{2}$

$\boxed{10 \text{ cm}}$

Step 2 — Calculate the height

Now we can use the Pythagorean theorem in one of the right-angled triangles.

The hypotenuse is the non-parallel side, which is 26 cm.

The base of the triangle is 10 cm, as we found in the previous step.

Let's call the height $h$.

$h^2 = (\text{hypotenuse})^2 - (\text{base})^2$

$h^2 = (26 \text{ cm})^2 - (10 \text{ cm})^2$

$h^2 = 676 \text{ cm}^2 - 100 \text{ cm}^2$

$h^2 = 576 \text{ cm}^2$

$h = \sqrt{576 \text{ cm}^2}$

$\boxed{24 \text{ cm}}$

Step 3 — Calculate the area

We now have all the values needed to find the area of the trapezium.

The formula for the area of a trapezium is $\frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$.

The parallel sides are 40 cm and 20 cm.

The height is 24 cm.

$= \frac{1}{2} \times (40 \text{ cm} + 20 \text{ cm}) \times 24 \text{ cm}$

$= \frac{1}{2} \times 60 \text{ cm} \times 24 \text{ cm}$

$= 30 \text{ cm} \times 24 \text{ cm}$

$\boxed{720 \text{ cm}^2}$

Answer

(i) The area of the trapezium is $720 \text{ cm}^2$.