We read your photo as:

Calculate the area and perimeter of a shape that is a semicircle with a straight base of diameter 4 m.

Mathematics

ScanSolve AI Answer

Step-by-step solution

3 steps
  1. Identify the shape and its dimensions.

    The image shows a shape that is a semicircle with a straight base.
    The length of the straight base, which is the diameter of the semicircle, is given as 4 m.
    The radius rr of the semicircle is half of its diameter.

    r=4 m2=2 mr = \frac{4 \text{ m}}{2} = 2 \text{ m}
  2. Calculate the area (Question 3).

    The area of a semicircle is given by the formula 12πr2\frac{1}{2} \pi r^2.
    Substitute the value of rr:

    Area=12π(2 m)2\text{Area} = \frac{1}{2} \pi (2 \text{ m})^2 Area=12π(4 m2)\text{Area} = \frac{1}{2} \pi (4 \text{ m}^2) Area=2π m2\text{Area} = 2\pi \text{ m}^2

    Using the approximation π≈3.14\pi \approx 3.14:

    Area≈2×3.14 m2=6.28 m2\text{Area} \approx 2 \times 3.14 \text{ m}^2 = 6.28 \text{ m}^2

    The area is 2π m2≈6.28 m2\boxed{2\pi \text{ m}^2 \approx 6.28 \text{ m}^2}.

  3. Calculate the perimeter (Question 4).

    The perimeter of this shape consists of two parts: the curved arc length of the semicircle and the straight diameter.
    The arc length of a semicircle is πr\pi r.
    The diameter is 2r2r.

    Perimeter=πr+2r\text{Perimeter} = \pi r + 2r

    Substitute the value of rr:

    Perimeter=π(2 m)+2(2 m)\text{Perimeter} = \pi (2 \text{ m}) + 2(2 \text{ m}) Perimeter=2π m+4 m\text{Perimeter} = 2\pi \text{ m} + 4 \text{ m} Perimeter=(2π+4) m\text{Perimeter} = (2\pi + 4) \text{ m}

    Using the approximation π≈3.14\pi \approx 3.14:

    Perimeter≈(2×3.14+4) m=(6.28+4) m=10.28 m\text{Perimeter} \approx (2 \times 3.14 + 4) \text{ m} = (6.28 + 4) \text{ m} = 10.28 \text{ m}

    The perimeter is (2π+4) m≈10.28 m\boxed{(2\pi + 4) \text{ m} \approx 10.28 \text{ m}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp