In an isosceles trapezoid ABCD, the perimeter is 42 cm, the lateral side is 10 cm.

| January 10, 2021 | education

In an isosceles trapezoid ABCD, the perimeter is 42 cm, the lateral side is 10 cm. Find the area of the trapezoid if its acute angle is equal.

Let’s draw the heights of the ВК and CH trapezoid.
In the right-angled triangle СDН, the angle of DCH = (180 – 90 – 60) = 300. Then the kate of the DН is located opposite the angle of 300, and therefore, DН = СD / 2 = 10/2 = 5 cm.
Since the trapezoid is isosceles, then AK = DН = 5 cm.
CH ^ 2 = СD ^ 2 – DН ^ 2 = 100 – 25 = 75.
CH = √75 = 5 * √3 cm.
The perimeter of the trapezoid is 42 cm.
AB + BC + СD + AD= 42 cm.
BC + AD = 42 – 10 – 10 = 22 cm.
AD= (AK + KH + DH) = (KH + 10) = (BC + 10).
Sun + Sun + 10 = 22.
2 * BC = 12 cm.
BC = 12/2 = 6 cm.
Then AD = 5 + 6 + 5 = 16 cm.
The area of the trapezoid is equal to: Savsd = (BC + AD) * СН / 2 = (6 + 16) * 5 * √3 / 2 = 55 * √3 cm2.
Answer: The area of the trapezoid is 55 * √3 cm2.



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