To find the area of each pool, we need to break down the complex shapes into simpler geometric figures like rectangles, triangles, trapezoids, and semicircles. Then we calculate the area of each part and add them together.
Here is the step-by-step calculation for each pool:
Pool #1
This shape is an octagon that can be split into three parts: a large rectangle in the middle and two identical trapezoids on the top and bottom.
1.
Middle Rectangle:
* Length = $19.4 \text{ ft}$
* Width (height) = $8 \text{ ft}$ (based on the side label)
* $\text{Area} = 19.4 \times 8 = 155.2 \text{ sq ft}$
2.
Top and Bottom Trapezoids:
* These are identical. Let's calculate one and multiply by 2.
* Height = $5.7 \text{ ft}$
* Base 1 (long side) = $19.4 \text{ ft}$
* Base 2 (short side) = $8 \text{ ft}$
* $\text{Area of one trapezoid} = \frac{(19.4 + 8)}{2} \times 5.7$
* $\text{Area} = \frac{27.4}{2} \times 5.7 = 13.7 \times 5.7 = 78.09 \text{ sq ft}$
* $\text{Area of both trapezoids} = 78.09 \times 2 = 156.18 \text{ sq ft}$
3.
Total Area for Pool #1:
* $155.2 + 156.18 = \mathbf{311.38 \text{ sq ft}}$
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Pool #2
This shape consists of a square and a semicircle attached to one side.
1.
The Square:
* Side length = $22 \text{ ft}$
* $\text{Area} = 22 \times 22 = 484 \text{ sq ft}$
2.
The Semicircle:
* The diameter of the semicircle is the side of the square, which is $22 \text{ ft}$.
* Radius ($r$) = $\frac{22}{2} = 11 \text{ ft}$
* $\text{Area of a full circle} = \pi \times r^2 = 3.14159 \times 11^2 = 3.14159 \times 121 \approx 380.13 \text{ sq ft}$
* $\text{Area of the semicircle} = \frac{380.13}{2} \approx 190.07 \text{ sq ft}$
3.
Total Area for Pool #2:
* $484 + 190.07 = \mathbf{674.07 \text{ sq ft}}$
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Pool #3
This shape is composed of a parallelogram on top and a right-angled triangle on the bottom.
1.
The Parallelogram (Top Part):
* Base = $18 \text{ ft}$
* Height = $12 \text{ ft}$ (indicated by the dashed line)
* $\text{Area} = \text{Base} \times \text{Height} = 18 \times 12 = 216 \text{ sq ft}$
2.
The Triangle (Bottom Part):
* Base = $18 \text{ ft}$ (shared with the parallelogram above)
* Height = $11 \text{ ft}$
* $\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = 0.5 \times 18 \times 11$
* $\text{Area} = 9 \times 11 = 99 \text{ sq ft}$
3.
Total Area for Pool #3:
* $216 + 99 = \mathbf{315 \text{ sq ft}}$
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Final Answer:
Pool #1: 311.38 sq ft
Pool #2: 674.07 sq ft
Pool #3: 315 sq ft
Parent Tip: Review the logic above to help your child master the concept of composite figure.
