Sketch the nets of the following pyramids and hence work out the surface area of each. Pyramid (c) has a square base with side length 12 cm and slant edges of 10 cm.

You're on a roll — here is the solution for part (c). 1. Sketch the nets of the following pyramids and hence work out the surface area of each. Pyramid (c): Net: The net consists of a square base with side length 12 cm. Attached to each side of this square are four isosceles triangles. Each isosceles triangle has a base of 12 cm and two equal sides (slant edges) of 10 cm. Surface Area Calculation: Step 1: Calculate the area of the square base. A_base = (12 cm)^2 = 144 cm^2 Step 2: Calculate the height of one isosceles triangular face (this is the slant height of the pyramid). For an isosceles triangle with base b=12 cm and equal sides l=10 cm, the height h_t can be found using the Pythagorean theorem: h_t = sqrt(l^2 - ((b)/(2))^2) = sqrt((10 cm))^2 - (6 cm)^2 = sqrt(100 cm)^2 - 36 cm^2 = sqrt(64) cm = 8 cm Step 3: Calculate the area of one isosceles triangular face. A_triangle = (1)/(2) × base × height_t = (1)/(2) × 12 cm × 8 cm = 48 cm^2 Step 4: Calculate the total area of the four triangular faces (lateral surface area). A_lateral = 4 × 48 cm^2 = 192 cm^2 Step 5: Calculate the total surface area by adding the base area and the lateral surface area. A_total = A_base + A_lateral = 144 cm^2 + 192 cm^2 = 336 cm^2 The surface area is 336 cm^2 Drop the next question!