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What is the perimeter of a semicircle with a base of 0.7 m?

Mathematics

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Answer

1.799 m\text{1.799 m}

Step-by-step solution

3 steps

Okay, let's tackle from the image. I'll assume you're looking for the perimeter of the shape.

  1. Identify the shape and its dimensions.

    The shape is a semicircle with a straight base.
    The length of the straight base is given as 0.7 m. This also represents the diameter of the semicircle.
    The radius of the semicircle is half of the diameter: r=0.7 m2=0.35 mr = \frac{0.7 \text{ m}}{2} = 0.35 \text{ m}.

  2. Calculate the length of the curved part.

    The curved part is a semicircle, so its length is half the circumference of a full circle. The formula for the circumference of a full circle is C=2πrC = 2\pi r.
    Length of curved part Lcurve=12×2πr=πrL_{curve} = \frac{1}{2} \times 2\pi r = \pi r.
    Using π≈3.14\pi \approx 3.14:

    Lcurve=3.14×0.35 mL_{curve} = 3.14 \times 0.35 \text{ m} Lcurve=1.099 mL_{curve} = 1.099 \text{ m}
  3. Calculate the total perimeter.

    The total perimeter of the shape is the sum of the length of the curved part and the length of the straight base.

    P=Lcurve+base lengthP = L_{curve} + \text{base length} P=1.099 m+0.7 mP = 1.099 \text{ m} + 0.7 \text{ m} P=1.799 mP = 1.799 \text{ m}

    The perimeter of the shape is 1.799 m\text{1.799 m}.

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