In a rectangular trapezoid, the bases are 6 cm and 9 cm, and the large side is 5 cm. Find the area of this trapezoid.

Given:
ABCE – rectangular trapezoid,
BC = 6 centimeters,
AE = 9 centimeters,
CE = 5 centimeters.
Find the area of ​​the trapezoid ABCE, that is, S ABCE -?
Decision:
1. Consider a rectangular trapezoid ABCE. Let’s draw the CO height. We get a rectangle ABCO. He has AB = CO and BC = CO = 6 centimeters. Then EO = 9 – 6 = 3 (centimeters).
2. Consider a right-angled triangle COE.
By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
CO ^ 2 + OE ^ 2 = CE ^ 2;
CO ^ 2 + 9 = 25;
CO ^ 2 = 16;
CO = 4 centimeters.
3. The area of ​​the trapezoid ABCE, that is, S ABCE = 1/2 * (BC + AE) * CO = 1/2 * (6 + 9) * 4 = 2 * 15 = 30 cm ^ 2.
Answer: 30 cm ^ 2.