In trapezoid ABCD, it is known that AD = 8, BC = 3, and its area is 77. Find the area of triangle ABC.

Let’s build the height BH of the trapezoid ABCD.

Knowing the area of the trapezoid and the length of its bases, we determine the length of the height BH.

Savsd = (ВС + АD) * ВН / 2.

BH = 2 * Sfvsd / (BC + AD) = 2 * 77 / (3 + 8) = 2 * 7 = 14 cm.

Let’s draw the height AK of triangle ABC. The height of the AK of the triangle is equal to the height BH of the trapezoid BACD, since the quadrilateral AKBH is a rectangle. Then AK = BH = 14 cm.

Determine the area of the triangle ABC.

Savs = BC * AK / 2 = 3 * 14/2 = 21 cm2.

Answer: The area of triangle ABC is 21 cm2.