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Difficulty: HardPerimeter and Area of 2D Figures

A municipal park has a flat rectangular section and a semi-circular section attached to one of the rectangle's shorter sides. The overall length of the park, measured from the straight edge of the rectangle to the farthest curved point of the semi-circle, is 200200 meters. The width of the rectangular section is 100100 meters. What is the outer perimeter of the entire park in meters? (Use π≈3.14\pi \approx 3.14)

  1. A
    657657
  2. B
    714714
  3. 557557Answer
  4. D
    18,92518,925

Answer

The outer perimeter of the park is 557557 meters.
The perimeter is the total distance around the outside of the shape. First, find the radius of the semi-circle, which is half of its 100100-meter diameter (5050 m). Subtract this radius from the total 200200-meter length to find the straight edge of the rectangle (150150 m). The outer boundary consists of one 100100-meter straight edge, two 150150-meter straight edges, and the semi-circular arc. The arc length is half the circumference of a full circle (0.5×3.14×100=1570.5 \times 3.14 \times 100 = 157 m). Adding these outer edges together gives 100+150+150+157=557100 + 150 + 150 + 157 = 557 meters.

Step-by-Step Solution

1
Identify the diameter and radius of the semi-circle.
Diameter = 100100 m, Radius = 5050 m
The semi-circle is attached to the 100100-meter wide side of the rectangle, so its diameter matches that width.
2
Determine the length of the rectangular section's straight sides.
200−50=150200 - 50 = 150 m
The overall length (200200 m) includes both the rectangle's length and the semi-circle's radius (5050 m).
3
Calculate the arc length of the semi-circular section.
12×π×d=0.5×3.14×100=157\frac{1}{2} \times \pi \times d = 0.5 \times 3.14 \times 100 = 157 m
The outer curved edge is exactly half of a full circle's circumference.
4
Sum the lengths of all outer boundary segments.
100+150+150+157=557100 + 150 + 150 + 157 = 557 m
The total perimeter includes one short straight edge (100100 m), two long straight edges (150150 m each), and the curved arc (157157 m). The internal dashed line is not part of the outer perimeter.

Key Concept

Calculating unknown dimensions and outer perimeters of composite figures.
Estimated Time:1m 0s
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Topics

Perimeter and Area of 2D Figures

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