Find the area of a rectangular trapezoid, the bases of which are 9 and 11, the large side makes

Find the area of a rectangular trapezoid, the bases of which are 9 and 11, the large side makes an angle of 45 degrees with the base.

1. The tops of the trapezoid – A, B, C, D. CE – height. S is the area of the trapezoid. ∠D = 45 °. ∠А = ∠В = 90 °.

BC = 9 units. AD = 11 units.

2. BC = AE, since in the rectangle ABCE the opposite sides are equal.

3. DE = AD – AE = 11 – 9 = 2 units.

4. We calculate the length of the CE height through the tangent ∠D:

CE: DE = tangent ∠D = tangent 45 ° = 1.

CE = DE x 1 = 2 x 1 = 2 units.

5. S = (BC + AD) / 2 x CE = (9 + 11) / 2 x 2 = 20 units of measurement².

Answer: S equals 20 units².