Koopa Troopa throws a dart at a parallelogram-shaped board, shown below. You know that $BC=10$, $AE=4$, and angle $BAD=45^\circ$. Assuming the dart will hit all spots on the board with equal likelihood, what is the probability the dart lands in triangle $ABE$? Express your answer as a decimal between 0 and 1.

Guest Aug 3, 2018

#4**0 **

Since angle BAD =45 degrees, so is angle ABE, because it is a right triangle. Its height BE=4

Area =BC x BE(Height)

= 10 x 4

** = 40 units^2 - the area of parallelogram.**

**Area of triangle ABE =1/2 x 4 x 4 =8 units^2**

**The probability that the dart will land in triangle ABE =8/40 =0.2**

Guest Aug 3, 2018

edited by
Guest
Aug 3, 2018