Determine the total surface area of the figure below. The figure is a prism with a triangular base. The height of the triangle is 5 cm, the base of the triangle is 12 cm, and the length of the prism is 20 cm.

Question

Asked on July 12, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-07-12T13:10:03.960Z

Ili kupata eneo lote la uso wa umbo hili, tutahitaji kuhesabu eneo la kila uso na kisha kuyajumlisha. Umbo hili ni mche (prism) wenye sehemu ya msalaba (cross-section) inayoundwa na mstatili na nusu duara. Vipimo vilivyotolewa ni: • Urefu wa mstatili = 5 cm • Upana wa mstatili (na kipenyo cha nusu duara) = 12 cm • Urefu wa mche = 20 cm Step 1: Tafuta eneo la sehemu ya msalaba (cross-section). Sehemu ya msalaba ina mstatili na nusu duara. Eneo la mstatili = urefu × upana A_mstatili = 12 cm × 5 cm = 60 cm^2 Kipenyo cha nusu duara ni 12 cm, hivyo rediasi r = (12)/(2) = 6 cm. Eneo la nusu duara = (1)/(2) r^2 A_nusu\_duara = (1)/(2) (6 cm)^2 = (1)/(2) (36 cm^2) = 18 cm^2 Eneo la sehemu ya msalaba, A_cs = A_mstatili + A_nusu\_duara A_cs = (60 + 18) cm^2 Step 2: Hesabu eneo la nyuso mbili za mwisho (sehemu za msalaba). Kuna nyuso mbili za mwisho zinazofanana. Eneo la nyuso mbili za mwisho = 2 × A_cs A_mwisho = 2(60 + 18) cm^2 = (120 + 36) cm^2 Step 3: Hesabu eneo la uso wa chini wa mstatili. Uso wa chini una urefu wa 20 cm na upana wa 12 cm. A_chini = 12 cm × 20 cm = 240 cm^2 Step 4: Hesabu eneo la nyuso mbili za pembeni za mstatili. Kila uso wa pembeni una urefu wa 20 cm na upana wa 5 cm. A_pembeni = 2 × (5 cm × 20 cm) = 2 × 100 cm^2 = 200 cm^2 Step 5: Hesabu eneo la uso wa juu uliopinda (nusu silinda). Mzingo wa nusu duara ni r = (6 cm) = 6 cm. Eneo la uso uliopinda = (mzingo wa nusu duara) × (urefu wa mche) A_pinda = (6 cm) × 20 cm = 120 cm^2 Step 6: Jumlisha maeneo yote ili kupata eneo lote la uso. Eneo lote la uso (TSA) = A_mwisho + A_chini + A_pembeni + A_pinda TSA = (120 + 36) + 240 + 200 + 120 TSA = (120 + 240 + 200) + (36 + 120) TSA = 560 + 156 cm^2 Step 7: Badilisha thamani ya ≈ 3.142 na hesabu jibu la namba. TSA = 560 + 156 × 3.142 TSA = 560 + 490.152 TSA = 1050.152 cm^2 Ukizungusha hadi sehemu moja ya desimali: TSA ≈ 1050.2 cm^2 Eneo lote la uso wa umbo hilo ni: 1050.2 cm^2 Tuma swali linalofuata 📸

Accepted Answer · 2026-07-12T13:10:03.960Z

Ili kupata eneo lote la uso wa umbo hili, tutahitaji kuhesabu eneo la kila uso na kisha kuyajumlisha. Umbo hili ni mche (prism) wenye sehemu ya msalaba (cross-section) inayoundwa na mstatili na nusu duara. Vipimo vilivyotolewa ni: • Urefu wa mstatili = 5 cm • Upana wa mstatili (na kipenyo cha nusu duara) = 12 cm • Urefu wa mche = 20 cm Step 1: Tafuta eneo la sehemu ya msalaba (cross-section). Sehemu ya msalaba ina mstatili na nusu duara. Eneo la mstatili = urefu × upana A_mstatili = 12 cm × 5 cm = 60 cm^2 Kipenyo cha nusu duara ni 12 cm, hivyo rediasi r = (12)/(2) = 6 cm. Eneo la nusu duara = (1)/(2) r^2 A_nusu\_duara = (1)/(2) (6 cm)^2 = (1)/(2) (36 cm^2) = 18 cm^2 Eneo la sehemu ya msalaba, A_cs = A_mstatili + A_nusu\_duara A_cs = (60 + 18) cm^2 Step 2: Hesabu eneo la nyuso mbili za mwisho (sehemu za msalaba). Kuna nyuso mbili za mwisho zinazofanana. Eneo la nyuso mbili za mwisho = 2 × A_cs A_mwisho = 2(60 + 18) cm^2 = (120 + 36) cm^2 Step 3: Hesabu eneo la uso wa chini wa mstatili. Uso wa chini una urefu wa 20 cm na upana wa 12 cm. A_chini = 12 cm × 20 cm = 240 cm^2 Step 4: Hesabu eneo la nyuso mbili za pembeni za mstatili. Kila uso wa pembeni una urefu wa 20 cm na upana wa 5 cm. A_pembeni = 2 × (5 cm × 20 cm) = 2 × 100 cm^2 = 200 cm^2 Step 5: Hesabu eneo la uso wa juu uliopinda (nusu silinda). Mzingo wa nusu duara ni r = (6 cm) = 6 cm. Eneo la uso uliopinda = (mzingo wa nusu duara) × (urefu wa mche) A_pinda = (6 cm) × 20 cm = 120 cm^2 Step 6: Jumlisha maeneo yote ili kupata eneo lote la uso. Eneo lote la uso (TSA) = A_mwisho + A_chini + A_pembeni + A_pinda TSA = (120 + 36) + 240 + 200 + 120 TSA = (120 + 240 + 200) + (36 + 120) TSA = 560 + 156 cm^2 Step 7: Badilisha thamani ya ≈ 3.142 na hesabu jibu la namba. TSA = 560 + 156 × 3.142 TSA = 560 + 490.152 TSA = 1050.152 cm^2 Ukizungusha hadi sehemu moja ya desimali: TSA ≈ 1050.2 cm^2 Eneo lote la uso wa umbo hilo ni: 1050.2 cm^2 Tuma swali linalofuata 📸

Determine the total surface area of the figure below. The figure is a prism with a triangular base. The height of the triangle is 5 cm, the base of the triangle is 12 cm, and the length of the prism is 20 cm.

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Determine the total surface area of the figure below. The figure is a prism with a triangular base. The height of the triangle is 5 cm, the base of the triangle is 12 cm, and the length of the prism is 20 cm.

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