Find the area of an isosceles trapezoid if its smaller base is 18 cm h = 9 cm, acute angle = 45 °

Given:
isosceles trapezoid ABCE,
BC = 18 centimeters,
ВН- height,
BH = 9 centimeters,
angle BAE = 45 degrees.
Find S ABCE -?
Solution:
1. Let’s draw the height of the CК. Received a BCКN rectangle. BC = НK = 18 centimeters.
2. Right-angled triangle ABН = right-angled triangle СKE by hypotenuse and angle, since angle A = angle E, BA = CE. So AH = KE = 9 centimeters.
3. Consider a right-angled triangle ABН. Angle ABH = 180 – 45 – 90 = 45 (degrees). Then triangle AHB is isosceles. Therefore BH = HA = 9 centimeters.
4. Base AE = AH + НK + KE = 9 + 18 + 9 = 36 (centimeters).
5.S ABCE = (BC + AE) * BH = (18 + 36) / 2 * 9 = 243 cm ^ 2.
Answer: 243 cm ^ 2.