# the diagram shows the plan view of a swimming pool. The pool has a rectangular swimming area and a semi-circle area with steps. Work out the total surface area of the top of the pool. Giver your answer to 3 significant figures.

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## no diagram, but

area of rectangle is length * width
area of semicircle is 1/2 π * width*2

subtract one from the other.

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## To calculate the total surface area of the pool, we need to find the area of the rectangular swimming area and the area of the semi-circle area with steps, and then add them together.

Step 1: Calculate the area of the rectangular swimming area
We can find the area of a rectangle by multiplying its length (L) by its width (W).
Let's assume that the length of the rectangular swimming area is L and the width is W.

Area of rectangular swimming area = L * W

Step 2: Calculate the area of the semi-circle area with steps
The semi-circle area with steps can be divided into two parts: a semi-circle and a rectangle.

The area of a semi-circle is found by multiplying the square of its radius (r) by half of the value of pi (π/2).
Let's assume that the radius of the semi-circle area is r.

Area of semi-circle = (π/2) * (r^2)

The rectangular part of the semi-circle area can be calculated using the length and width of the rectangular swimming area.

Area of rectangular part = L * W

Step 3: Add the two areas together to get the total surface area

Total surface area = Area of rectangular swimming area + Area of semi-circle + Area of rectangular part

Total surface area = L * W + (π/2) * (r^2) + L * W

Finally, calculate the total surface area by substituting the values of the length, width, and radius of the pool.

Please provide the values of L, W, and r to proceed with the calculation.

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## To find the total surface area of the top of the pool, we need to calculate the surface area of the rectangular swimming area and the semi-circle area with steps separately, and then add them together.

1. Surface area of the rectangular swimming area:
The surface area of a rectangle can be calculated by multiplying its length by its width. In this case, the length of the rectangular swimming area is the longer side of the pool, and its width is the shorter side.
Let's assume the length of the rectangular swimming area is L meters, and the width is W meters.

Surface area of the rectangular swimming area = L * W

2. Surface area of the semi-circle area with steps:
The surface area of a semi-circle can be calculated by multiplying half of its circumference (πr) by its radius (r), and adding the area of its flat rectangular section.
Let's assume the radius of the semi-circle area is R meters, and the width of the flat rectangular section is also W meters (same as the width of the swimming area).

Circumference of the semi-circle = 2πR
Area of the semi-circle = 1/2 * πR * R
Area of the flat rectangular section = W * R

Surface area of the semi-circle area with steps = (1/2 * πR * R) + (W * R)

3. Total surface area of the pool:
To find the total surface area of the pool, we add the surface areas of the rectangular swimming area and the semi-circle area with steps.

Total surface area = Surface area of the rectangular swimming area + Surface area of the semi-circle area with steps

Total surface area = (L * W) + ((1/2 * πR * R) + (W * R))

Now, you can substitute the actual measurements (L, W, and R) into the equation to find the total surface area of the top of the pool.

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