The surface area of a three dimensional object is the sum of the areas of all its faces. Here we have a net of triangular prism, which if we were to fold would form a three dimensional shape.
We need to find the area of each face. Let's begin with the rectangle in the center which can be found by calculating its length times width:
26 * 10 = 260 in^2
Next, let's find the area of the other two rectangles. Although it does not specify that these rectangles are congruent (meaning the same), we know that they are because if they were different sizes, the prism would not fit together when folded. We can find the area of one rectangle and multiply by two:
26 * 13 = 338
338 * 2 = 676 in^2
Lastly, we have two triangles which are congruent for the same reason as the rectangles. The area of a triangle can be found by calculating one-half the base time the height:
0.5 * 10 * 12 = 60
Times two since there are two triangles:
60 * 2 = 120 in^2
Add up the areas:
260 + 676 + 120 = 1056 in^2
Multiply the surface area by 6 because there are 6 packages:
This can be solved by using the binomial distribution. The probability of guessing correctly is 0.5, and the probability of making a wrong guess is also 0.5.
