To find the area of the playground, we will break the shape into simpler components.

Given dimensions:

• The shape consists of a trapezoid and a rectangle.
• The rectangle on the left has dimensions 6 ft × 6 ft.
• The trapezoid has bases 18 ft and 30 ft, with a height of 6 ft.

Step 1: Find the area of the rectangle

$A_{\text{rectangle}} = \text{length} \times \text{width} = 6 \times 6 = 36 \text{ ft}^2$

Step 2: Find the area of the trapezoid

The area of a trapezoid is given by: $A_{\text{trapezoid}} = \frac{1}{2} \times ( \text{Base}_1 + \text{Base}_2 ) \times \text{Height}$ Substituting values: $A_{\text{trapezoid}} = \frac{1}{2} \times (18 + 30) \times 6$ $= \frac{1}{2} \times 48 \times 6$ $= 144 \text{ ft}^2$

Step 3: Total area

$A_{\text{total}} = A_{\text{rectangle}} + A_{\text{trapezoid}}$ $= 36 + 144$ $= 180 \text{ ft}^2$

Final Answer:

180 square feet

Would you like a breakdown of any step?

Here are some related questions to explore:

1. How do you find the perimeter of this playground?
2. What is the area of a similar shape if all dimensions are doubled?
3. How can you find the volume if this playground is covered with sand 1 ft deep?
4. How does the area formula for a trapezoid compare to a parallelogram?
5. If fencing costs $5 per square foot, what is the total cost to cover this playground?

Tip: Breaking complex shapes into simpler ones like rectangles and trapezoids makes area calculations easier!