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Below is a plot of land. Study it carefully and answer the questions that follow. a) Find the perimeter of the plot ( p=3.14) b) Workout the area covered by the plot.

Mathematics

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Answers

2 parts
a

162.8m\text{}162.8\text{m}

b

1428m2\text{}1428\text{m}^2\text{}

Step-by-step solution

6 steps

Huu ni mchoro wa shamba lenye umbo la mstatili na nusu duara.

Part a· 3 steps

Kupata mzunguko wa shamba

Mzunguko ni jumla ya urefu wa kingo za nje za umbo.
Kutoka kwenye mchoro:

  • Urefu wa upande wa kushoto (upana wa mstatili) ni 20m20\text{m}.
  • Urefu wa upande wa juu (urefu wa mstatili) ni 40m40\text{m}.
  • Urefu wa upande wa chini ni 60m60\text{m}.
  • Mstari wa doti unaonyesha rediasi ya nusu duara, ambayo ni sawa na upana wa mstatili, r=20mr = 20\text{m}.
  • Sehemu ya chini ya mstatili ni 60m−r=60m−20m=40m60\text{m} - r = 60\text{m} - 20\text{m} = 40\text{m}.
  • Urefu wa upinde wa nusu duara ni πr\pi r.

  1. Tambua vipimo vya pande za nje.

    Urefu wa upande wa kushoto = 20m20\text{m}
    Urefu wa upande wa juu = 40m40\text{m}
    Urefu wa upande wa chini wa mstatili = 40m40\text{m}
    Rediasi ya nusu duara, r=20mr = 20\text{m}

  2. Kokotoa urefu wa upinde wa nusu duara.

    Urefu wa upinde=πr\text{Urefu wa upinde} = \pi r Urefu wa upinde=3.14×20m\text{Urefu wa upinde} = 3.14 \times 20\text{m} Urefu wa upinde=62.8m\text{Urefu wa upinde} = 62.8\text{m}

  3. Jumlisha urefu wa pande zote za nje ili kupata mzunguko.

    Mzunguko=20m+40m+40m+62.8m\text{Mzunguko} = 20\text{m} + 40\text{m} + 40\text{m} + 62.8\text{m} Mzunguko=162.8m\text{Mzunguko} = 162.8\text{m}

    Mzunguko wa shamba ni 162.8m\boxed{\text{}162.8\text{m}}.

Part b

1428m2\text{}1428\text{m}^2\text{}

Kokotoa eneo lililofunikwa na shamba

Eneo la shamba ni jumla ya eneo la mstatili na eneo la nusu duara.

  1. Kokotoa eneo la mstatili.

    Urefu wa mstatili = 40m40\text{m}
    Upana wa mstatili = 20m20\text{m}

    Eneo la mstatili=urefu×upana\text{Eneo la mstatili} = \text{urefu} \times \text{upana} Eneo la mstatili=40m×20m\text{Eneo la mstatili} = 40\text{m} \times 20\text{m} Eneo la mstatili=800m2\text{Eneo la mstatili} = 800\text{m}^2

  2. Kokotoa eneo la nusu duara.

    Rediasi ya nusu duara, r=20mr = 20\text{m}

    Eneo la nusu duara=12πr2\text{Eneo la nusu duara} = \frac{1}{2} \pi r^2 Eneo la nusu duara=12×3.14×(20m)2\text{Eneo la nusu duara} = \frac{1}{2} \times 3.14 \times (20\text{m})^2 Eneo la nusu duara=12×3.14×400m2\text{Eneo la nusu duara} = \frac{1}{2} \times 3.14 \times 400\text{m}^2 Eneo la nusu duara=3.14×200m2\text{Eneo la nusu duara} = 3.14 \times 200\text{m}^2 Eneo la nusu duara=628m2\text{Eneo la nusu duara} = 628\text{m}^2

  3. Jumlisha eneo la mstatili na eneo la nusu duara.

    Jumla ya eneo=Eneo la mstatili+Eneo la nusu duara\text{Jumla ya eneo} = \text{Eneo la mstatili} + \text{Eneo la nusu duara} Jumla ya eneo=800m2+628m2\text{Jumla ya eneo} = 800\text{m}^2 + 628\text{m}^2 Jumla ya eneo=1428m2\text{Jumla ya eneo} = 1428\text{m}^2

    Eneo lililofunikwa na shamba ni 1428m2\boxed{\text{}1428\text{m}^2\text{}}.

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