i) The suitable name for the above roof is a rectangular pyramid. This is because its base is a rectangle (with dimensions 12 cm and 8 cm) and its sides meet at a single apex.

Here is the solution to your problem: Task i) The suitable name for the above roof is a rectangular pyramid. This is because its base is a rectangle (with dimensions 12 cm and 8 cm) and its sides meet at a single apex. ii) Step 1: Calculate the length AV. Assuming the pyramid is a right pyramid with equal slant edges, and given BV = CV = DV = 20 cm from the problem statement and diagram, then: AV = 20 cm Step 2: Calculate the height OV. First, find the length of the diagonal of the base, AC. Using the Pythagorean theorem in ABC: AC^2 = AB^2 + BC^2 AC^2 = (12 cm)^2 + (8 cm)^2 AC^2 = 144 cm^2 + 64 cm^2 AC^2 = 208 cm^2 AC = sqrt(208) cm = sqrt(16 × 13) cm = 4sqrt(13) cm The point O is the center of the rectangular base, so OC is half the diagonal AC: OC = (1)/(2) AC = (1)/(2) (4sqrt(13) cm) = 2sqrt(13) cm Now, use the Pythagorean theorem in the right-angled triangle OVC to find the height OV: OV^2 + OC^2 = CV^2 OV^2 + (2sqrt(13) cm)^2 = (20 cm)^2 OV^2 + (4 × 13) cm^2 = 400 cm^2 OV^2 + 52 cm^2 = 400 cm^2 OV^2 = 400 cm^2 - 52 cm^2 OV^2 = 348 cm^2 OV = sqrt(348) cm = sqrt(4 × 87) cm = 2