Cost of Edging for Flower Garden

MathematicsGeometryMedium

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Answer the following questions on refill. 1. The flower garden will be surrounded by wooden garden edging that is sold in 5 metre lengths. Each 5 metre roll of edging costs $63.99. How much will it cost to surround the flower garden with this edging?

This question includes visual content: A diagram shows a large park area (green) with several white cutouts representing features: a circular cutout at the top-left, a flower garden with rounded edges, a square fountain in the center, and a large L-shaped playground. Dimensions are provided for the entire boundary (bottom width 60 m, total height 50 m, top edge 46 m, right lower segment 22 m). The flower garden has a width of 7 m, two long sides of 15 m and 11.5 m, and a base of 7.94 m.

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Step 1

Hi Keita, let's solve this problem together. We need to find the total cost of the wooden edging required to surround the flower garden.

The Flower Garden

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Step 2

First, let's identify the components of the garden's perimeter. It consists of a semi-circular top and three straight edges: the left side, the bottom, and the right side.

$$Perimeter = \text{Arc} + 11.5 + 7.94 + 15$$
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Step 3

The top is a semi-circle with a diameter of 7 metres. The length of this semi-circular arc is half of pi times the diameter.

$$\text{Arc} = 0.5 \times \pi \times 7 \approx 10.996 \text{ m}$$
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Step 4

Now we add this to the straight sides to find the total perimeter.

$$P = 10.996 + 11.5 + 7.94 + 15 = 45.436 \text{ m}$$

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About This Question

Subject
Mathematics
Topic
Geometry
Difficulty
Medium
Question Type
Open Ended

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