Question

Given Rectangle ABCD. E is the midpoint of Line DC and F is the midpoint of Line DA. The area of Triangle DEF is what fraction of the area of Rectangle ABCD?

(A) 1 / 8
(B) 1 / 4
(C) 1 / 2
(D) 1

Answer 1

The area of Triangle DEF is 1/8 the area of Rectangle ABCD because each side of Triangle DEF is half the length of the corresponding sides of the rectangle.

Step-by-step explanation:

The area of Triangle DEF is 1/8 the area of Rectangle ABCD. Since E and F are midpoints of sides DC and DA respectively, side EF is parallel to side BC and half its length. Triangle DEF is therefore a right triangle with its legs being half the length of the rectangle's sides.

The area of a rectangle is calculated by the formula length × width, and the area of a triangle is 1/2 × base × height. In this case, the base and height of Triangle DEF are each half the length and width of Rectangle ABCD. This makes the area of Triangle DEF 1/4 of half the area of Rectangle ABCD, yielding a fraction of 1/8.

We can visualize this by recognizing that four congruent triangles of DEF could fit within Rectangle ABCD, filling half its area. Another set of four identical triangles would fill the other half. Hence, one Triangle DEF is 1/8th of the total rectangle's area.