A square-based pyramid has a volume of 384 m3 and a base side length of 12 m. Calculate (a) the number of triangular faces, (b) the height of the pyramid, and (c) the slant height.

You're on a roll — here are the solutions to the questions: a) A square-based pyramid has a square base and four triangular faces that meet at the apex. There are 4 triangular surfaces. 4 triangular surfaces b) Step 1: Calculate the area of the square base. The length of each side of the base is l = 12 m. The base area A_b is given by: A_b = l^2 = (12 m)^2 = 144 m^2 Step 2: Use the formula for the volume of a pyramid to find the height h. The volume V of a pyramid is given by V = (1)/(3) A_b h. Given V = 384 m^3: 384 m^3 = (1)/(3) (144 m^2) h 384 m^3 = 48 m^2 · h Step 3: Solve for h. h = 384 m^348 m^2 = 8 m The height of the tent is 8 m. 8 m c) Step 1: Calculate the slant height s of the pyramid. The height h = 8 m (from part b) and half the base side length is (l)/(2) = 12 m2 = 6 m. Using the Pythagorean theorem, s^2 = h^2 + ((l)/(2))^2: s^2 = (8 m)^2 + (6 m)^2 s^2 = 64 m^2 + 36 m^2 s^2 = 100 m^2 s = sqrt(100 m)^2 = 10 m Step 2: Calculate the area of one triangular face. The base of each triangle is l = 12 m and the slant height is s = 10 m. Area of one triangle = (1)/(2) × base × slant height A_triangle = (1)/(2) × 12 m × 10 m = 60 m^2 Step 3: Calculate the total cloth required (lateral surface area). Since there are 4 triangular faces, the total cloth required is: Total cloth = 4 × A_triangle = 4 × 60 m^2 = 240 m^2 The amount of cloth required to construct the tent is 240 m^2. 240 m^2 What's next? 🤔