Find the area of a rectangular trapezoid with a base of 3 cm and 6 cm and an angle of 135 degrees.

1. Vertices of the trapezoid – A, B, C, D. ∠А = ∠В = 90 °. ∠С = 135 °. ВС = 3 cm. АD = 6 cm. СН – height.

S is the area of the trapezoid.

2. Considering that the sum of the angles of a quadrilateral (in this problem – a trapezoid) is 360 °,

calculate the value ∠D:

∠D = 360 ° – ∠А – ∠В – ∠С = 360 ° – 90 ° – 90 ° – 135 ° = 45 °.

3. BC = AN as opposite sides of the rectangle ABCH.

4.DН = АD – АН = 6 – 3 = 3 cm.

5.CH = DH x tangent ∠D = 3 x tangent 45 ° = 3 x 1 = 3 cm.

6. S = (BC + AD) / 2 x CH = (3 + 6) / 2 x 3 = 13.5 cm².