The playground consists of three different shapes: a square $TSVU$, a trapezium $SRQV$, and a parallelogram $PQVU$.

To calculate the total area of the playground, we will find the areas of these three shapes individually and then sum them.

1. Square $TSVU$

• Given: Side length of the square is 20 m (from $TS$).
• The area of a square is given by: $\text{Area of square} = \text{side}^2 = 20^2 = 400 \, \text{m}^2$

2. Trapezium $SRQV$

• The parallel sides of the trapezium are $SR = 45 \, \text{m}$ and $VQ = 40 \, \text{m}$ (from diagram).
• The height of the trapezium is the vertical distance from $S$ to $V$, which is 20 m (the same as the side of the square).
• The area of a trapezium is given by: $\text{Area of trapezium} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$ Substituting values: $\text{Area of trapezium} = \frac{1}{2} \times (45 + 40) \times 20 = \frac{1}{2} \times 85 \times 20 = 850 \, \text{m}^2$

3. Parallelogram $PQVU$

• The base of the parallelogram is $PQ = 40 \, \text{m}$.
• The height of the parallelogram is the vertical distance from $V$ to $U$, which is the same as the side of the square, 20 m.
• The area of a parallelogram is given by: $\text{Area of parallelogram} = \text{Base} \times \text{Height} = 40 \times 20 = 800 \, \text{m}^2$

4. Total Area of the Playground

• Now, summing the areas of the three shapes: $\text{Total area} = 400 + 850 + 800 = 2050 \, \text{m}^2$

Thus, the total area of the playground is 2050 square meters.

Would you like a detailed breakdown of any step?

Here are 5 related questions to consider:

1. How would the area change if the side of the square were 25 m instead of 20 m?
2. What is the perimeter of the entire playground?
3. Can the formula for a trapezium be derived using geometry principles?
4. What would happen to the trapezium's area if the height increased to 30 m?
5. How does the shape of the parallelogram affect the calculation of the area?

Tip: When dealing with composite shapes, break them down into simpler figures, calculate their areas individually, and then sum them for the total area.