In an isosceles trapezoid, the bases are 8 cm and 16 cm, and the angle at the base is 45 degrees.

| January 10, 2021 | education

In an isosceles trapezoid, the bases are 8 cm and 16 cm, and the angle at the base is 45 degrees. What is the area of the trapezoid?

Given:
isosceles trapezoid ABCE,
BC = 8 centimeters,
AE = 16 centimeters,
angle A = angle E = 45 degrees.
Find the area of ​​the trapezoid ABCE, that is, S ABCE -?
Decision:
1. Consider an isosceles trapezoid ABCE. Let’s draw the heights of HВ and CO. We get the HBCO rectangle. He has ВН = CO and BC = HC = 8 centimeters.
2. Right-angled triangle ABН = right-angled triangle COE along the hypotenuse and acute angle, since angle A = angle E and CE = AB. Then CE = AH = (16 – 8): 2 = 8: 2 = 4 (centimeters).
3. Consider the BHA triangle. Angle AВН = 180 – 90 – 45 = 45 (degrees). Then the triangle ABН is isosceles. So AH = HB = 4 centimeters.
4. The area of ​​the trapezoid ABCE, that is, S ABCE = 1/2 * (BC + AE) * BH = 1/2 * (8 + 16) * 4 = 2 * 24 = 48 cm ^ 2.
Answer: 48 cm ^ 2.



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