The area of a rectangular trapezoid is 120cm2, and its height is 8cm.

The area of a rectangular trapezoid is 120cm2, and its height is 8cm. Finds all sides of a trapezoid if one of the bases is 6cm larger than the other.

Given:
ABCE – rectangular trapezoid,
AB = 8 centimeters,
AE – BC = 6 centimeters,
S ABCE = 120 cm ^ 2.
Find BC, AE, CE -?
Solution:
Let BC = x centimeters, AE = x + 6 centimeters. Then
S ABCE = BA * (BC + AE) / 2;
120 = 8 * (x + x + 6) / 2;
120 = 4 * (x + x + 6);
30 = 2x + 6;
2x = 30 – 6;
2x = 24;
x = 24: 2;
x = 12 centimeters – aircraft length;
12 + 6 = 18 centimeters – AE length.
Consider a right-angled triangle HCE. By the Pythagorean theorem:
CE ^ 2 = CH ^ 2 + HE ^ 2;
CE ^ 2 = 64 + 36;
CE ^ 2 = 100;
CE = 10.
Answer: 12 centimeters; 18 centimeters; 10 centimeters.