Multiple choice

A right triangular prism has a right triangular base with legs measuring 3w centimeters and 4w centimeters. The area of the base is 6w2 square centimeters (cm2). The height of the prism is 10 cm. Which expression represents the surface area (in cm2) of the right triangular prism?

  1. 6w2 + 120w

  2. 12w2 + 210w

  3. 8w2 + 70w

  4. 12w2 + 120w
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Base area = 6w^2. Perimeter = 3w + 4w + 5w = 12w. Lateral area = Perimeter * height = 12w * 10 = 120w. Surface area = 2 * Base area + Lateral area = 2(6w^2) + 120w = 12w^2 + 120w.

AI explanation

The surface area of a right triangular prism is calculated by adding the lateral surface area, which is the perimeter of the base times the height of the prism, to the areas of the two triangular bases. The third side of the triangular base is found using the Pythagorean theorem, giving the square root of (3w squared plus 4w squared), which equals 5w, making the perimeter 12w. The lateral surface area is 12w times 10, resulting in 120w, and the combined area of the two bases is 2 times 6w squared, resulting in 12w squared. Combining these gives the total surface area expression of 12w squared plus 120w.

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