In an isosceles trapezoid, the side is 13 cm, the base 10 cm and 20 cm. Find the area of the trapezoid.

| November 18, 2020 | education

Given:
isosceles trapezoid ABCE,
BC = 10 centimeters,
AE = 20 centimeters,
AB = CE = 13 centimeters.
Find the area of ​​the trapezoid ABCE, that is, S ABCE -?
Decision:
1. Consider an isosceles trapezoid ABCE. Let’s draw the heights of HV and CO. We get the HBCO rectangle. He has VN = CO and BC = HO = 10 centimeters.
2. Right-angled triangle ABN = right-angled triangle SOE along the hypotenuse and acute angle, since angle A = angle E and CE = AB. Then OE = AH = (20 – 10): 2 = 10: 2 = 5 (centimeters).
3. Consider the BHA triangle. By the Pythagorean theorem: BH ^ 2 = AB ^ 2 – AH ^ 2 = 169 – 25 = 144, BH = 12 centimeters.
4. The area of ​​the trapezoid ABCE, that is, S ABCE = 1/2 * (BC + AE) * BH = 1/2 * (10 + 20) * 12 = 6 * 30 = 180 cm ^ 2.
Answer: 180 cm ^ 2.



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