The perimeter of the base of a right triangular prism is 44 cm and the height…
2025
The perimeter of the base of a right triangular prism is 44 cm and the height (length) of the prism is 8 cm. If the total surface area of the prism is 390 cm2, then what will be the total area of the two triangular bases?
Answer: C. 38 cm2 — For any right prism, the total surface area equals the lateral surface area plus the areas of the two identical bases: TSA = (Perimeter of base × Height) + 2…
- A.
20 cm2
- B.
30 cm2
- C.
38 cm2
- D.
28 cm2
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Correct answer: C
For any right prism, the total surface area equals the lateral surface area plus the areas of the two identical bases: TSA = (Perimeter of base × Height) + 2 × (Area of one base). This holds for any base shape, including a triangular base.
Given values: perimeter of the triangular base P = 44 cm, height (length) of the prism h = 8 cm, total surface area TSA = 390 cm2.
Lateral surface area = P × h = 44 × 8 = 352 cm2.
Total surface area = Lateral surface area + combined area of the two triangular bases, so 390 = 352 + (combined base area).
Combined base area = 390 − 352 = 38 cm2. This 38 cm2 already represents both triangular bases together (the formula's '2 × base area' term), so no further halving or doubling is needed.
Check: 352 (lateral surface area) + 38 (combined base area) = 390 cm2, matching the given total surface area — confirming the result.