# In trapezoid ABCD, the bases of AD and BC are 6 and 1, respectively, and its area is 42. Find the area of triangle ABC.

August 27, 2021 | education

| The area of the trapezoid is Sabcd = ((AD + BC) / 2) * h, where h is the height of the trapezoid.

From this formula we find the height of the trapezoid.

42 = (6 + 1) / 2 * h.

84 = 7 * h.

h = 12.

The area of the triangle ABC is found by the following formula:

Sabc = Sabcd – Sacd = 42 – ½ * AD * h = 42 – ½ * 6 * 12 = 42 – 36 = 6.

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.