Questions: A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 24 ft long and 18 ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? Do not round any intermediate computations. Round your final answer to the nearest hundredth and be sure to include the correct unit. If necessary, refer to the list of geometry formulas.

Solution Steps

The diameter of the semicircle is equal to the width of the rectangle, which is 18 ft. The radius is half the diameter, so the radius is 18 ft / 2 = 9 ft. The circumference of a full circle is 2πr. The circumference of the semicircle is half of that, plus the diameter (since the fence goes around the garden): (2π * 9 ft)/2 + 18 ft = 9π ft + 18 ft.

The fence goes around the three sides of the rectangle. The lengths of the sides needing fencing are 18 ft, 24 ft, and 18 ft. The total length of these sides is 18 ft + 24 ft + 18 ft = 60 ft.

The total fence required is the sum of the semicircle circumference and the perimeter of the rectangular section needing fence: (9π ft + 18 ft) + 60 ft = 9π ft + 78 ft ≈ 28.27 ft + 78 ft ≈ 106.27 ft

Final Answer