Multiple choice

Find the difference between the lateral and total surface area of a square-based pyramid with side $2.5$cm and slant height $8$cm.

  1. $6.25\ cm$
  2. $6.75\ cm$
  3. $6.68\ cm$
  4. $6.93\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total surface area of a square-based pyramid exceeds its lateral surface area by the area of its square base. The base area is 2.5^2 = 6.25 cm^2, so the numerical answer is 6.25.

AI explanation

Using the formulas for the lateral surface area (LSA) and total surface area (TSA) of a square-based pyramid, the LSA is (1/2) * (perimeter of base) * slant height and the TSA is LSA plus the base area. The LSA is (1/2) * (4 * 2.5) * 8 = 40 square cm, and the TSA is 40 + (2.5 * 2.5) = 46.25 square cm. The difference between the total and lateral surface areas is simply the area of the square base, which is 6.25 square cm.

Keep practicing — related questions