Question

En un cuadrado ABCD de lado 1, E es el punto medio de la diagonal BD y F punto medio de ED. ¿Cuál es el área del triángulo CFD?

Answer 1

The area of triangle CFD is 3/32 * sqrt(2)

Since E is the midpoint of BD, we have EB = EA = 1/2.

Since F is the midpoint of ED, we have EF = FD = 1/4.

Since triangle CFD is a right triangle, we can use the Pythagorean Theorem to find CF.

CF^2 = CD^2 - FD^2

CF^2 = (1/2)^2 - (1/4)^2

CF^2 = 3/16

CF = sqrt(3/16)

CF = 3/4 * sqrt(2)

The area of triangle CFD is 1/2 * CF * FD

The area of triangle CFD is 1/2 * (3/4 * sqrt(2)) * (1/4)

The area of triangle CFD is 3/32 * sqrt(2)

So the answer is 3/32 * sqrt(2)

Question

In a square ABCD of side 1, E is the midpoint of the diagonal BD and F is the midpoint of ED. What is the area of ​​the CFD triangle?