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

July 29, 2021 | education

| **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.

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