A triangular storage prism has a base shaped like a right triangle with side lengths in the ratio 5:12:13. If the total perimeter of the base is 60 cm and the height of the prism is 8 cm, calculate the lateral surface area of the prism.

Correct — C. The lateral faces are three rectangles, one on each side of the base, each 8 cm tall.

Sides: 60 ÷ (5 + 12 + 13) = 2 → 10, 24, 26 cm
Faces: 10×8 + 24×8 + 26×8 = 80 + 192 + 208
Lateral area = 480 cm² → option (c)

Shortcut: base perimeter × height = 60 × 8 = 480. The ratio is not needed.

Why the others are wrong

• (a)
  360 cm² — 360 cm² matches no combination of the faces (80, 192, 208 cm²). Divided by the height it gives a perimeter of 45 cm, not the stated 60 cm.
• (b)
  300 cm² — 300 cm² ÷ 8 = 37.5 cm of perimeter, far short of 60 cm. No sum of the three faces gives 300.
• (d)
  400 cm² — 400 cm² is the two larger faces only: 24×8 + 26×8 = 192 + 208. It leaves out the 10 cm × 8 cm face, 80 cm².

A right prism has two identical end faces joined by rectangular side faces. Lateral surface area = base perimeter × height, because the side faces unroll into one rectangle, here 60 cm long and 8 cm tall.

Total surface area adds the two ends. The base is a right triangle with legs 10 and 24, so its area is ½ × 10 × 24 = 120 cm² and the TSA is 480 + 2 × 120 = 720 cm².

Key facts

• Lateral surface area of a right prism = base perimeter × height.
• Total surface area = lateral area + 2 × base area.
• 5² + 12² = 13², so sides in the ratio 5:12:13 always form a right triangle.
• Volume of a prism = base area × height.

Common traps

• Adding the two triangular ends. That gives the total surface area, 720 cm², not the lateral area.
• Counting only two of the rectangular faces, which gives 400 cm².

No directly related past PYQ was found.