Multiple choice

What is the total surface area of a pyramid whose base is a square with side 8 cm and height of the pyramid is 3 cm?

  1. 169 cm2

  2. 121 cm2

  3. 144 cm2

  4. 184 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Base area = 8*8 = 64. Slant height (s) = sqrt(h^2 + (side/2)^2) = sqrt(3^2 + 4^2) = 5. Lateral area = 4 * (1/2 * base * s) = 2 * 8 * 5 = 80. Total surface area = 64 + 80 = 144.

AI explanation

To find the total surface area, first determine the slant height of the pyramid using the Pythagorean theorem on the right triangle formed by the pyramid's height, half the base, and the slant height. The slant height is the square root of (3^2 + 4^2), which equals 5 cm. The area of the square base is 8 * 8 = 64 square cm, and the area of the four triangular faces is 4 * (1/2) * base * slant height, or 4 * (1/2) * 8 * 5 = 80 square cm. Adding the base area and the triangular faces gives a total surface area of 144 square cm.

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