A right square pyramid has a square base of side 10 cm and vertical height 12
cm. Find: (i) its volume, (ii) its slant height, (iii) its lateral surface area.

(i) Volume of a pyramid = (1/3) × (area of base) × height Base area = 10 × 10 = 100 cm² Volume = (1/3) × 100 × 12 = 400 cm³ (ii) Slant height l is the height of a triangular face. In right square pyramid, l is the hypotenuse of right triangle with one leg = vertical height h = 12, other leg = half the base side = 5. l = √(h² + (side/2)²) = √(12² + 5²) = √(144 + 25) = √169 = 13 cm (iii) Lateral surface area = sum of areas of 4 congruent triangular faces. Area of one triangle = (1/2) × base × slant height = (1/2) × 10 × 13 = 65 cm² Lateral surface area = 4 × 65 = 260 cm²