The height of the trapezoid is 20 cm, and the area is 440 cm2. Find the midline and base

| May 3, 2021 | education

The height of the trapezoid is 20 cm, and the area is 440 cm2. Find the midline and base of the trapezoid if one base is 1.2 times longer than the other.

Let’s construct a trapezoid ABCD, in which:

BC = x (smallest base of a trapezoid)

AD = 1.2x (largest base, by convention 1.2 times longer than BC)

BH = 20 cm (trapezoid height)

S ABCD = 440 cm2 (trapezoidal area)

KN =? (middle line of a trapezoid)

From the formula for finding the area of the trapezoid, we compose the equation:

S = (BC + AD / 2) * BH

440 = (x + 1.2x / 2) * 20

x + 1.2x / 2 = 22

2.2x = 44

x = 20

Therefore: BC = 20 cm

AD = 1.2 * 20 = 24 cm

Find the middle line of the trapezoid using the formula

KN = BC + AD / 2

KN = 20 + 24/2

KN = 22 cm

Answer: 20cm and 24.cm are the bases, 22cm is the middle line of the trapezoid.



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