What is the surface area of a right triangle prism with legs measuring 4 and 8 and a height of 12

Answer 1

Surface area is simply the sum of the areas of each side, which means we must first isolate each side, measure it, then add all the sides' measurements to get the final total. A prism is a solid, three-dimensional object - with width, length, and height. Area is the measure of a two-dimensional object, such as a piece of land or a surface. That it is a triangle tells us that the height is on one side only, and there is an hypotenuse running down from the height to the base. If the measurements are 4, 8, and 12, we know the area of the base is 4x8 (32) and the area of the upright side is 4x12 (48). There's a trick we can use to find the area of the two, large sides: pretend that it is a rectangle, find the area, then divide by two. These right triangles are halves of rectangles measuring 8x12. If the area of a rectangle is 8x12 (96), half of it is 48. So far, we have four sides: the base (32), the upright (48), and the left and right sides (48 each). The total so far is 176 (32+48+48+48).

Now we need the measurement of the hypotenuse, so we can find the area of the last remaining side. Remember the Pythagorean Theorem? A-squared plus B-squared equals C-squared? That is what we need to do this. We will use length and height to find the measure of the hypotenuse, as the width does not relate at all to the area of the two, large sides. If A=8 and B=12, then A-squared equals 64 and B-squared equals 144. We add these two numbers (208), then find the square root (14.422). We can now find the final measurement of this figure's surface area. The width (4) times the hypotenuse (14.422) gives us the measure of that side's area (57.688), which we then add to the previous total (176). 176+57.688=233.688