The quadrilateral in the given figure is ABCD squared. The midpoints AB and BC are P and Q, respectively. So tell the probability of choosing the inside point of the triangle PQD. [AB = BC = CD = DA = 6]
Answers
Since you are using midpoints this isn’t as tough as you might have thought.
Let’s say that the square is 2x2 just to make the arithmetic easier. The area of the square therefore is 4.
To get the area of triangle AEF, we can subtract the areas of the other 3 triangles formed from the 4 for the square, remembering that the area of a triangle is (bxh)/2.
Since all three of the other triangles are right triangles this is not difficult. Triangle ABE is (2x1)/2 = 1, Triangle ADF is also (2x1)/2 = 1, and triangle FCE is (1x1)/2 which is 1/2.
The total is 2.5 so area of triangle AEF is 1.5,
The ratio would be 1.5 to 4, but we prefer that be written as 3 to 8 or 3/8.
Step-by-step explanation:
Since you are using midpoints this isn’t as tough as you might have thought.
Let’s say that the square is 2x2 just to make the arithmetic easier. The area of the square therefore is 4.
To get the area of triangle AEF, we can subtract the areas of the other 3 triangles formed from the 4 for the square, remembering that the area of a triangle is (bxh)/2.
Since all three of the other triangles are right triangles this is not difficult. Triangle ABE is (2x1)/2 = 1, Triangle ADF is also (2x1)/2 = 1, and triangle FCE is (1x1)/2 which is 1/2.
The total is 2.5 so area of triangle AEF is 1.5,
The ratio would be 1.5 to 4, but we prefer that be written as 3 to 8 or 3/8.