The height of an isosceles trapezoid is h, its smaller base is a. Find the perimeter and area of the trapezoid if the side is 2h?

univerkov | January 4, 2021 | education

From the right-angled triangle CDH, by the Pythagorean theorem, we determine the length of the leg of the DH.
DN^2 = CD^2 – CH^2 = 4 * h2 – h2 = 3 * h2.
DH = h * √3 cm.
Since the trapezoid is isosceles, the ABP and CDH triangles are equal in hypotenuse and acute angles, then AP + DH = 2 * h * √3 cm.
Then AD = AP
Determine the length of the larger base.
AD = (AR + DH + PH) = a + h * √3 + h * √3 = a + 2 * h * √3 cm.
Then Ravsd = AB + BC + CD + AD = 2 * h + a + 2 * h + a + 2 * h * √3 = 2 * a + 4 * h + 2 * h * √3 = 2 * a + 2 * h * (2 + √3) see.
Determine the area of the trapezoid.
Savsd = (BC + AD) * CH / 2 = (a + a + 2 * h * √3) * h / 2 = h * (a + h * √3) cm2.
Answer: The area of the trapezoid is h * (a + h * √3) cm2, the perimeter is 2 * a + 2 * h * (2 + √3) cm.

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