In the figure, each side of square ABCD has length 1, the length of li

3 rules and concepts:

(1) in an isosceles triangle, the height drawn from the Vertex between the two equal sides perpendicular to he non-equal side will Bisect the non-equal side and will act as a the Median

(2) the Median, in any triangle, divides the triangle into 2 sub-triangles that have Equal Area

(3) for an obtuse triangle such as triangle BCE, you can take the height outside of the triangle by drawing a line from Vertex B perpendicular to a straight line extended from Base Side CE


The diagonal of the square = (side) * sqrt(2)

Connect the square’s diagonal from B to D = (1) * sqrt(2)


This gives you Isosceles Triangle BED

Next, extend the Median from Vertex E to side BD.

This Median, because it is between the 2 equal sides of the Isosceles Triangle, will meet BD at a perpendicular Angle.

Call the point where the Median hits BD —- point X

If we take Side CE as the Base of Triangle BCE

Then BX will be the perpendicular height drawn from the opposite Vertex B ———> which will equal (1/2) the Diagonal of the Square ———> (1/2) * sqrt(2)

Using side CE = 1 as the Base of the Triangle, this will be the perpendicular height.


Area of triangle BCE will therefore be:

(1/2) * (1) * (1/2) * sqrt(2)

Or

Sqrt(2) * (1/4)

Answer B

Posted from my mobile device