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Find the area (π = 22/7)

Mathematics

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Answer

273 cm2\text{273 cm}^2

Step-by-step solution

3 steps

Hapa kuna suluhisho la swali lako:

Mchoro unaonyesha umbo lililounganishwa, linalojumuisha nusu duara (semi-circle) na trapeza (trapezium). Tunahitaji kupata eneo la jumla la umbo hili.

  1. Hesabu eneo la nusu duara.

    Kutoka kwenye mchoro, kipenyo cha nusu duara ni 14 cm. Hivyo, rediasi (rr) ni 142=7\frac{14}{2} = 7 cm.
    Tunatumia π=227\pi = \frac{22}{7}.

    Eneo la nusu duara=12πr2\text{Eneo la nusu duara} = \frac{1}{2} \pi r^2 Eneo la nusu duara=12×227×(7 cm)2\text{Eneo la nusu duara} = \frac{1}{2} \times \frac{22}{7} \times (7 \text{ cm})^2 Eneo la nusu duara=12×227×49 cm2\text{Eneo la nusu duara} = \frac{1}{2} \times \frac{22}{7} \times 49 \text{ cm}^2 Eneo la nusu duara=11×7 cm2\text{Eneo la nusu duara} = 11 \times 7 \text{ cm}^2 Eneo la nusu duara=77 cm2\text{Eneo la nusu duara} = 77 \text{ cm}^2
  2. Hesabu eneo la trapeza.

    Trapeza ina pande mbili sambamba zenye urefu wa 10 cm na 18 cm. Urefu (height) wa trapeza ni 14 cm.

    Eneo la trapeza=12(a+b)h\text{Eneo la trapeza} = \frac{1}{2} (a+b) h

    Ambapo a=10 cma = 10 \text{ cm}, b=18 cmb = 18 \text{ cm}, na h=14 cmh = 14 \text{ cm}.

    Eneo la trapeza=12(10 cm+18 cm)×14 cm\text{Eneo la trapeza} = \frac{1}{2} (10 \text{ cm} + 18 \text{ cm}) \times 14 \text{ cm} Eneo la trapeza=12(28 cm)×14 cm\text{Eneo la trapeza} = \frac{1}{2} (28 \text{ cm}) \times 14 \text{ cm} Eneo la trapeza=14 cm×14 cm\text{Eneo la trapeza} = 14 \text{ cm} \times 14 \text{ cm} Eneo la trapeza=196 cm2\text{Eneo la trapeza} = 196 \text{ cm}^2
  3. Hesabu eneo la jumla.

    Eneo la jumla ni jumla ya eneo la nusu duara na eneo la trapeza.

    Eneo la jumla=Eneo la nusu duara+Eneo la trapeza\text{Eneo la jumla} = \text{Eneo la nusu duara} + \text{Eneo la trapeza} Eneo la jumla=77 cm2+196 cm2\text{Eneo la jumla} = 77 \text{ cm}^2 + 196 \text{ cm}^2 Eneo la jumla=273 cm2\text{Eneo la jumla} = 273 \text{ cm}^2

    Eneo la jumla la umbo ni 273 cm2\text{273 cm}^2.

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