In trapezoid ABCD, AD and BC-base. AD refers to BC as 2 refers to 1, point E
| March 26, 2021 | education
In trapezoid A B C D, AD and BC-base. AD refers to BC as 2 refers to 1, point E of the seridine of the trapezoid. Triangle area AED = 60cm ^ 2. Find the area of the entire trapezoid.
Point E is the middle of the middle line of the trapezoid, then the height of the trapezoid KH is equal to two heights EH of the triangle AED.
KN = 2 * EH.
The area of the triangle AED is equal to: Saed = AD * EH / 2.
The area of the trapezoid ABCD is equal to: Savsd = (BC + AD) * KN / 2
By condition ВС = АD / 2, and КН = 2 * ЕН.
Savsd = (AD / 2 + AD) * 2 * EH / 2 = 3 * AD * EH / 2 = 3 * Saed = 3 * 60 = 180 cm2.
Answer: The area of the trapezoid is 180 cm2.
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