This figure combines our knowledge of the surface area of pyramids and prisms. Oooh, fancy. First, let's figure out exactly what we want. The surface area of the overall figure consists of the lateral area of the pyramid and the lateral area of the prism along with one base (the bottom). We'll say the formula looks like this: SA = L_{Pyramid} + L_{Prism} + B Okay…but what do these things even mean? We'll start with the lateral area of the prism. Like we said in the last chapter, it's a folded rectangle where the length is the perimeter of the base and the height is...the height. The perimeter is 15 + 15 + 15 + 15 = 60 ft and the height is 20 ft. L_{Prism} = Ph L_{Prism} = (60 ft)(20 ft) = 1200 ft^{2} Moving on to the lateral area of the pyramid. Pyramids halve triangles, remember? The perimeter is the same, but l is the slant height, which is 15 ft. Two thirds done already? That's awesome. Trivia Time: Do we have to find the base of the prism or of the pyramid? It's actually a trick question because they're both the same. The base is a square no matter how you look at it. B = s^{2} B = (15 ft)^{2} B = 225 ft^{2} We have all the parts. All that's left is putting them together. SA = L_{Pyramid} + L_{Prism} + B SA = 450 ft^{2} + 1200 ft^{2} + 225 ft^{2} SA = 1875 ft^{2} |