The surface area of a solid refers to the total area around the outside of the solid. Usually, the quickest way to find the surface area of a solid is to find the area of all the faces around the object. In this shape, we have four rectangles and two trapezoids. This is illustrated below:
Rectangle at top:
Rectangle at the bottom:
Two trapezoids on the sides:
Two rectangles on the sides:
Lets find the areas of each of the four types of shapes and then add them up to get the total surface area:
The top rectangle has a length of 8 and a width of 6, so the area (length times width) is 8*6, or 48
The bottom rectangle has a length of 8 and a width of 3, so the area is 8*3, or 24
The formula for the area of a trapezoid is as follows:
Let's let the two bases of the trapezoid be a and b, and the height is h. The formula suggests that the area of a trapezoid is the average of the bases times the height. In the trapezoids we are given, the two bases are 3 and 6, and the height is 2.6. So, the are of ONE trapezoid is the following:
One trapezoid has an area of 11.7, and since there are two identical trapezoids, the total area of both is 11.7 * 2, which is 23.4
Finally, the area of one of the rectangles on the side has to be calculated. We know the length is 8 and the width is 3, so the area is 24. There are two rectangles, so the total area is 24 * 2 or 48.
To find the surface area, let's add up all the areas we have:
Therefore, the surface area is 143.4 mi^2