In the trapezoid ABCD AD = 9, BC = 3, and its area is 80. Find the area of the trapezoid BCNM

| February 16, 2021 | education

In the trapezoid ABCD AD = 9, BC = 3, and its area is 80. Find the area of the trapezoid BCNM, where MN is the middle line of the trapezoid ABCD.

Let’s find the length of the middle line of the trapezoid:
MN = (AD + BC) / 2 = (3 + 9) / 2 = 6.
The area of the trapezoid is equal to the product of the height of the trapezoid by its midline:
S = h * MN.
Where does the height come from: h = S / MN = 80/6.
The trapezoid BCNM is the upper part of the trapezoid ABCD, after dividing it by the middle line, that is, it has half the height:
h1 = h / 2 = (80/6) / 2 = 40/6 = 20/3
Bases of the new trapezium: MN and BC. The area of this trapezoid is equal to the product of the half-sum of the bases MN and BC by the height h1:
S1 = ((MN + BC) / 2) * h1 = ((6 + 3) / 2) * (20/3) = (9 * 20) / (2 * 3) = 30.



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.