# The area of a rectangular trapezoid is 24 cm ^ 2. The two smaller sides are equal

March 26, 2021 | education

| **The area of a rectangular trapezoid is 24 cm ^ 2. The two smaller sides are equal, and the acute angle is 45 degrees. Find the smaller base.**

Let the required base BC = X cm.

Then, by condition, AB = BC = X cm.

Let’s build the height of the CH trapezoid ABCD.

Quadrilateral ABCD is a rectangle with AB = BC, then this quadrilateral is a square. The triangle CDH is rectangular and isosceles, since the angle CDA, by condition, is equal to 45. Then DH = CH = BC = X cm.

The area of the trapezoid is equal to: Savsd = Savsn + Ssdn = AB * BC + CH * DH / 2 =

X ^ 2 + X ^ 2/2 = 24.

(2 * X ^ 2 + X ^ 2) / 2 = 24.

3 * X ^ 2 = 48.

X ^ 2 = 48/3 = 16.

X = BC = 4 cm.

Answer: The length of the smaller base is 4 cm.

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