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Zorluk: OrtaPerimeter and Area of Plane Shapes

A composite plane figure is formed by constructing a semicircle externally on one side of a square of side length 14 cm14\text{ cm}. What is the perimeter of the resulting figure? (Take π=227\pi = \frac{22}{7})

  1. 64 cm64\text{ cm}Cevap
  2. B
    78 cm78\text{ cm}
  3. C
    86 cm86\text{ cm}
  4. D
    50 cm50\text{ cm}

Cevap

64 cm64\text{ cm}
The outer perimeter of the composite shape consists of three straight edges of the square and one curved semicircular arc. Three sides of length 14 cm14\text{ cm} yield 42 cm42\text{ cm}. The arc length of a semicircle with radius 7 cm7\text{ cm} is πr=227×7=22 cm\pi r = \frac{22}{7} \times 7 = 22\text{ cm}. Adding these together gives 42 cm+22 cm=64 cm42\text{ cm} + 22\text{ cm} = 64\text{ cm}.

Adım Adım Çözüm

1
Identify the exposed straight sides of the square contributing to the perimeter.
The square has 4 sides, but 1 side is attached to the semicircle inside the figure. Thus, 3 sides are on the outer boundary: 3×14 cm=42 cm3 \times 14\text{ cm} = 42\text{ cm}.
Perimeter only includes the outer boundary of a composite shape.
2
Calculate the radius and arc length of the attached semicircle.
The diameter of the semicircle is equal to the side length of the square (d=14 cmd = 14\text{ cm}), so radius r=7 cmr = 7\text{ cm}. Semicircular arc length =πr=227×7=22 cm= \pi r = \frac{22}{7} \times 7 = 22\text{ cm}.
The curved boundary is half of the total circle circumference.
3
Sum the outer straight boundaries and the curved boundary.
Total perimeter =42 cm+22 cm=64 cm= 42\text{ cm} + 22\text{ cm} = 64\text{ cm}.
Combining all outer segment lengths gives the total perimeter.

Anahtar Kavram

Perimeter of composite plane figures involving straight line segments and circular arcs.
Tahmini Süre:1m 30s
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Perimeter and Area of Plane Shapes

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