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Calculate the area of the shaded parts.

Mathematics

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2 parts
a

512 cm2\text{512 cm}^2

b

468 cm2\text{468 cm}^2

Step-by-step solution

7 steps

Hapa kuna hatua za kukokotoa eneo la sehemu zenye kivuli:

Part a· 3 steps

  1. Kokotoa eneo la mstatili wa nje.

    Urefu wa mstatili wa nje ni 36 cm36 \text{ cm} na upana ni 24 cm24 \text{ cm}.

    Anje=urefu×upana=36 cm×24 cm=864 cm2A_{\text{nje}} = \text{urefu} \times \text{upana} = 36 \text{ cm} \times 24 \text{ cm} = 864 \text{ cm}^2

  2. Kokotoa eneo la mstatili wa ndani.

    Urefu wa mstatili wa ndani ni 22 cm22 \text{ cm} na upana ni 16 cm16 \text{ cm}.

    Andani=urefu×upana=22 cm×16 cm=352 cm2A_{\text{ndani}} = \text{urefu} \times \text{upana} = 22 \text{ cm} \times 16 \text{ cm} = 352 \text{ cm}^2

  3. Kokotoa eneo la sehemu yenye kivuli.

    Eneo lenye kivuli ni tofauti kati ya eneo la nje na eneo la ndani.

    Akivuli=Anje−Andani=864 cm2−352 cm2=512 cm2A_{\text{kivuli}} = A_{\text{nje}} - A_{\text{ndani}} = 864 \text{ cm}^2 - 352 \text{ cm}^2 = 512 \text{ cm}^2

    Eneo la sehemu yenye kivuli ni 512 cm2\boxed{\text{512 cm}^2}.

Part b

468 cm2\text{468 cm}^2

  1. Kokotoa eneo la mstatili wa nje.

    Urefu wa mstatili wa nje ni 42 cm42 \text{ cm} na upana ni 24 cm24 \text{ cm}.

    Anje=urefu×upana=42 cm×24 cm=1008 cm2A_{\text{nje}} = \text{urefu} \times \text{upana} = 42 \text{ cm} \times 24 \text{ cm} = 1008 \text{ cm}^2

  2. Kokotoa vipimo vya mstatili wa ndani.

    Urefu wa mstatili wa ndani: 42 cm−(6 cm+6 cm)=42 cm−12 cm=30 cm42 \text{ cm} - (6 \text{ cm} + 6 \text{ cm}) = 42 \text{ cm} - 12 \text{ cm} = 30 \text{ cm}.
    Upana wa mstatili wa ndani: 24 cm−(3 cm+3 cm)=24 cm−6 cm=18 cm24 \text{ cm} - (3 \text{ cm} + 3 \text{ cm}) = 24 \text{ cm} - 6 \text{ cm} = 18 \text{ cm}.

  3. Kokotoa eneo la mstatili wa ndani.

    Andani=urefu×upana=30 cm×18 cm=540 cm2A_{\text{ndani}} = \text{urefu} \times \text{upana} = 30 \text{ cm} \times 18 \text{ cm} = 540 \text{ cm}^2

  4. Kokotoa eneo la sehemu yenye kivuli.

    Eneo lenye kivuli ni tofauti kati ya eneo la nje na eneo la ndani.

    Akivuli=Anje−Andani=1008 cm2−540 cm2=468 cm2A_{\text{kivuli}} = A_{\text{nje}} - A_{\text{ndani}} = 1008 \text{ cm}^2 - 540 \text{ cm}^2 = 468 \text{ cm}^2

    Eneo la sehemu yenye kivuli ni 468 cm2\boxed{\text{468 cm}^2}.

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