In trapezoid ABCD AD = 4, BC = 1, and its area is 35. Find the area of triangle ABC.

Knowing the base of the trapezoid and its area, we find the height of the trapezoid. Let us denote the Bases of the BC through a = 1, AD through b = 3, the height – h, the area S = 35.

S = ((a + b) / 2) * h;

h = S / ((a + b) / 2);

h = 35 / ((1 + 4) / 2) = 35 / 2.5 = 14.

The height of the trapezoid is also the height of the triangle ABC. the base of this triangle is the side BC = a = 1.

SΔ = (ah) / 2;

SΔ = (1 * 14) / 2 = 14/2 = 7.

Answer 7.