Japuka eneo la umbo lililo hapo juu.

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ScanSolve AI Tutor · Accepted Answer

Hapa kuna hatua za kutafuta eneo la kila umbo:

Umbo la Kwanza (Chini):
Umbo hili linaweza kugawanywa katika mstatili tatu.

Tafuta eneo la mstatili wa kwanza (chini).
Urefu = $8 \text{ sm}$ , Upana = $2 \text{ sm}$ .
$\text{Eneo}_1 = \text{urefu} \times \text{upana} = 8 \text{ sm} \times 2 \text{ sm} = 16 \text{ sm}^2$
Tafuta eneo la mstatili wa pili (katikati).
Urefu = $6 \text{ sm}$ , Upana = $2 \text{ sm}$ .
$\text{Eneo}_2 = \text{urefu} \times \text{upana} = 6 \text{ sm} \times 2 \text{ sm} = 12 \text{ sm}^2$
Tafuta eneo la mstatili wa tatu (juu).
Urefu = $4 \text{ sm}$ , Upana = $2 \text{ sm}$ .
$\text{Eneo}_3 = \text{urefu} \times \text{upana} = 4 \text{ sm} \times 2 \text{ sm} = 8 \text{ sm}^2$
Jumlisha maeneo yote kupata eneo kamili la umbo.
$\text{Eneo Jumla} = \text{Eneo}_1 + \text{Eneo}_2 + \text{Eneo}_3 = 16 \text{ sm}^2 + 12 \text{ sm}^2 + 8 \text{ sm}^2 = 36 \text{ sm}^2$
Eneo kamili la umbo la kwanza ni $\boxed{\text{36 sm}^2}$ .

Umbo la Pili (Katikati):
Umbo hili linaweza kugawanywa katika mraba mmoja wa katikati na mstatili nne zinazouzunguka.
Tafuta eneo la mraba wa katikati.
Urefu = $5 \text{ sm}$ , Upana = $5 \text{ sm}$ .
$\text{Eneo}_{\text{mraba}} = \text{urefu} \times \text{upana} = 5 \text{ sm} \times 5 \text{ sm} = 25 \text{ sm}^2$
Tafuta eneo la mstatili mmoja wa pembeni.
Urefu = $5 \text{ sm}$ , Upana = $2 \text{ sm}$ .
$\text{Eneo}_{\text{mstatili mmoja}} = \text{urefu} \times \text{upana} = 5 \text{ sm} \times 2 \text{ sm} = 10 \text{ sm}^2$
Tafuta eneo la mstatili zote nne za pembeni.
Kuna mstatili nne, hivyo:
$\text{Eneo}_{\text{mstatili nne}} = 4 \times 10 \text{ sm}^2 = 40 \text{ sm}^2$
Jumlisha eneo la mraba na eneo la mstatili zote nne.
$\text{Eneo Jumla} = \text{Eneo}_{\text{mraba}} + \text{Eneo}_{\text{mstatili nne}} = 25 \text{ sm}^2 + 40 \text{ sm}^2 = 65 \text{ sm}^2$
Eneo kamili la umbo la pili ni $\boxed{\text{65 sm}^2}$ .

Umbo la Tatu (Juu):
Umbo hili lina pembetatu na nusu duara.
Tafuta eneo la pembetatu.
Msingi = $10 \text{ sm}$ , Kimo = $9 \text{ sm}$ .
$\text{Eneo}_{\text{pembetatu}} = \frac{1}{2} \times \text{msingi} \times \text{kimo} = \frac{1}{2} \times 10 \text{ sm} \times 9 \text{ sm} = 45 \text{ sm}^2$
Tafuta eneo la nusu duara.
Kipenyo = $10 \text{ sm}$ , hivyo rediasi $r = \frac{10 \text{ sm}}{2} = 5 \text{ sm}$ .
$\text{Eneo}_{\text{nusu duara}} = \frac{1}{2} \times \pi \times r^2 = \frac{1}{2} \times \pi \times (5 \text{ sm})^2 = \frac{1}{2} \times \pi \times 25 \text{ sm}^2 = 12.5 \pi \text{ sm}^2$
Kutumia $\pi \approx 3.14159$ :
$12.5 \pi \text{ sm}^2 \approx 12.5 \times 3.14159 \text{ sm}^2 \approx 39.27 \text{ sm}^2$
Jumlisha eneo la pembetatu na eneo la nusu duara.
$\text{Eneo Jumla} = \text{Eneo}_{\text{pembetatu}} + \text{Eneo}_{\text{nusu duara}} = 45 \text{ sm}^2 + 12.5 \pi \text{ sm}^2$ $\text{Eneo Jumla} \approx 45 \text{ sm}^2 + 39.27 \text{ sm}^2 = 84.27 \text{ sm}^2$
Eneo kamili la umbo la tatu ni $\boxed{\text{45} + 12.5\pi \text{ sm}^2 \approx 84.27 \text{ sm}^2}$ .

Japuka eneo la umbo lililo hapo juu.

Step-by-step solution

Tafuta eneo la mstatili wa kwanza (chini).

Tafuta eneo la mstatili wa pili (katikati).

Tafuta eneo la mstatili wa tatu (juu).

Jumlisha maeneo yote kupata eneo kamili la umbo.

Tafuta eneo la mraba wa katikati.

Tafuta eneo la mstatili mmoja wa pembeni.

Tafuta eneo la mstatili zote nne za pembeni.

Jumlisha eneo la mraba na eneo la mstatili zote nne.

Tafuta eneo la pembetatu.

Tafuta eneo la nusu duara.

Jumlisha eneo la pembetatu na eneo la nusu duara.

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