Find the area of an isosceles trapezoid if its smaller base is 10 cm, its height is 9 cm and the acute angle is 45 degrees

Consider a right-angled triangle СНD, which, according to the condition, has an СDН angle = 450, then the DСН angle = 180 – 90 – 45 = 450. The angles at the base of the СD are equal to each other, therefore the СНD triangle is isosceles, СН = DН = 9 cm.
And the vertices B will draw the height ВM, which will cut off the segment AM, which will be equal to the segment DН, since the trapezoid is isosceles.
Determine the length of the base of the blood pressure. AD = AM + MН + DН = 9 + 10 + 9 = 28 cm.
Then the area of the trapezoid is: S = (AD + BC) * CH / 2 = 28 * 9/2 = 126 cm2.
Answer: S = 126 cm2.

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