There are a few more eccentric structures that have triangular shapes on the top and bottom, like this.įortunately, calculating the surface area of these structures, known as prisms, is very similar to what we’ve already done.īut in this case, we just have three sides and a top and bottom. Not all of the buildings in the city, however, are shaped like boxes and cubes. We can start with the formula we found for the surface area of a box.īut since the length, width, and height of a cube are all the same, we can use the same value to calculate the area of each face.Ī cube has the same number of faces as a box, but each has the area of side times side, so we can simply multiply 6 times the length of a side squared, to obtain the total surface area. The process of finding surface area for a box is often represented by the formula: Surface area equals two times the length times width, plus two times the height times length, plus two times the width times height.īut this can be written shorter by using the first letter of each dimension like this.įinding the surface area of a cube is very similar, and a bit easier. This time, we multiply the width of 50 feet times the length, 85 feet, giving us 4,250 square feet.Īgain, we multiply this result by two, providing us with an additional 8,500 square feet.īy summing all the areas, we get the total surface area of the building.īut, since we don't have to cover the bottom of the building in salt, we can subtract the surface area of the base, giving us 55,550 square feet. The only thing that’s left is the top and bottom. Multiplying a height of 190 feet times a width of 50 feet, we get 9,500 square feet.Īgain, we multiply this result by two to get 19,000 square feet, since there is another face that's the same size. This gives us 32,300 square feet.īy rotating the box a bit, we see that there are two more areas that need to be calculated. If we just look at this face of the building, the length is 85 feet and the height is 190 feet.īut this was just the front face, so we need to multiply it by two to get the back face as well. The area of each face is calculated by multiplying the two dimensions that make up the face, length times height, height times width, or width times length. Surface area is just the sum of the areas of each of the faces. There’s a top and bottom, a right and left face, and a front and back face. The calculations for the surface area of cubes and boxes are not so different from each other. However, to get the math just right, the director needs our help with calculating the surface area of prisms, cubes and boxes. In order to save the city, he hatches a plan to cover all the buildings in a thin layer of salt, which will protect the city from the slugs’ slime. In Torpintino’s new movie, a famous scientist, Navy SEAL, and men’s fashion model is elected President, but on his first day in office, the world is attacked by an onslaught of really, really big space slugs. He’s pitching his latest idea to a big time studio executive: Attack of the Really, Really Big Slugs from Outer Space, but the studio executive needs a bit of convincing. Sam Torpintino is an aspiring movie director who is looking for his big break.
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