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

September 29, 2021 | education

| 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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.