Calculating the Remaining Area of a Park
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What is the total area of this?
This question includes visual content: The image shows a large irregular green polygon representing a park. It has a circular cut-out in the top-left corner (radius 14m), a square 'Fountain' ($5m imes 5m$), a rectangular 'Playground' (with segments measuring 20m, 28m, 7m, 5m), and an oddly shaped 'Flower garden' (with dimensions 11.5m, 7m, 7.94m, 15m). The overall boundary of the park is defined by sides measuring 46m, 50m, 60m, and 22m.
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Hi Keita, let's work through this composite area problem step by step by separating the large boundary from the cut out regions inside it.
Find the Total Shaded Area
We will calculate the area of the outer shape first, then subtract the areas of the empty regions.
From the diagram, the outside boundary can be treated as a large rectangle with a triangular corner removed, and also a semicircular notch on the left side.
The full height is fifty meters plus the fourteen meter semicircle diameter, giving a total height of sixty four meters.
Now substitute the values into the outer area expression.
So the outer shaded boundary has an area of about three thousand four hundred sixty nine square meters.
Next, let's find the area of the playground, which is an L shaped region.
Playground Area
The large rectangle measures twenty eight by twenty, and the missing top right rectangle has width twenty three and height seven.
Multiplying gives one hundred sixty one for the missing rectangle.
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