In a rectangular trapezoid, the smaller side is 6 cm and makes an angle of 45 degrees with the smaller diagonal

In a rectangular trapezoid, the smaller side is 6 cm and makes an angle of 45 degrees with the smaller diagonal. The acute angle of the trapezoid is also 45 degrees. Find the area of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. AB = 6 cm – smaller lateral side. AC – smaller diagonal. Angle BAC = 45 °. Angle D = 45 °.

2. Angle ACB = 180 ° – 45 ° – 90 ° = 45 °. Since the angles at the base of the AC are equal, triangle ABC is isosceles. AB = BC = 6 cm.

3. From the top of C we draw the height BH.

4. Angle DСН = 180 ° – 45 ° – 90 ° = 45 °. The CDH triangle is also isosceles. CH = DH = 6 cm.

5. AD = DH + AH.

AH = BC = 6 cm.

AD = 6 + 6 = 12 cm.

6. The area of the trapezium ABCD = (BC + AD) / 2 x CH = (6 + 12) / 2 x 6 = 54 cm ^ 2.