In rectangle ABCD, side AD is 10, vertex A is connected to the middle
| March 3, 2021 | education
In rectangle ABCD, side AD is 10, vertex A is connected to the middle of the opposite side BC, and tg of angle AEB = 0.6. Find the area of the trapezoid AECD
ABCD rectangle, then BC = AD = 10 cm.
Since, by condition, point E is the middle of the segment BC, then BE = CE = BC / 2 = 10/2 = 5 cm.
From the right-angled triangle ABE, through the angle and the leg, we determine the size of the leg AB.
tgBAE = AB / BE.
AB = BE * tgBAE = 5 * 0.6 = 3 cm.
Then the height EH of the trapezoid is equal to AB. EH = AB = 3 cm.
Determine the area of the trapezoid.
Saesd = (EC + AD) * EH / 2 = (5 + 10) * 3/2 = 22.5 cm2.
Answer: The area of the trapezoid is 22.5 cm2.
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