The perimeter of the figure below is 120 metres. What is the area of the figure?

The figure is an L-shape. The perimeter of such a figure, when it can be enclosed in a rectangle, is equal to the perimeter of its enclosing rectangle.
From the image, the overall width of the figure is given as $(6x+30)$ m.
The overall height of the figure is given as $(5x-20)$ m.

The perimeter $P$ of the enclosing rectangle is $2 \times (\text{width} + \text{height})$.
We are given $P = 1120$ metres.

Divide both sides by 2:

Subtract 10 from both sides:

Divide by 11:

Overall width $W = 6x+30 = 6(50)+30 = 300+30 = 330 \text{ m}$.
Overall height $H = 5x-20 = 5(50)-20 = 250-20 = 230 \text{ m}$.

The question asks for the area of "the figure". Given the multiple-choice options, it is highly probable that the question is asking for the area of the enclosing rectangle rather than the exact L-shape, as the area of the L-shape does not match any option.
Area of the enclosing rectangle $= \text{Width} \times \text{Height}$

This matches option D.

The final answer is $\text{75900}$.