To find the probability that the dart lands in the shaded region, we can use the following formula,
P(dart in shaded region) = (Area of shaded region) / (Total area of the dartboard)
This is because the dart has equal probability of landing anywhere on the board. Therefore, we just need to find the ratio of the shaded region, to the entire board.
First, let's calculate the area of the entire board. Notice that the bottom of the diagram shows 6 equal measures of 2 units, so the length is 12, and width is given on the right hand side as 3.
A = L x W = 12 x 3 = 36
Now, let's find the area of a single shaded region. I will leave it to you to research how the area of a parallelogram is calculated, but for the purposes of this problem, I can tell you that it is as simple as multiplying the side length on the bottom (2) by the height of the parallelogram (3), which is 6.
So, there are 3 regions with an area of 6. Therefore, the total shaded area is 3 x 6 = 18
Now we can calculate the probability of the dart landing in the shaded region using the first formula,
P(dart in shaded region) = (Area of shaded region) / (Total area of the dartboard)
P(dart in shaded region) = 18 / 36 = 1 / 2
So the probability is 1 / 2 or 50%.
