What is the height of a trapezium given the area is 60 cm², the top base is 10 cm, and the bottom base is 20 cm?

To find the height of a trapezium when given the area and the lengths of the two bases, we can use the formula for the area of a trapezium:

[

\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

]

In this case, the area is 60 cm², the top base (Base₁) is 10 cm, and the bottom base (Base₂) is 20 cm. Plugging these values into the formula, we have:

[

60 = \frac{1}{2} \times (10 + 20) \times \text{Height}

]

This simplifies to:

[

60 = \frac{1}{2} \times 30 \times \text{Height}

]

[

60 = 15 \times \text{Height}

]

To isolate the height, divide both sides by 15:

[

\text{Height} = \frac{60}{15} = 4 \text{ cm}

]

Thus, the height of the trapezium is 4 cm. This confirms that the