In an isosceles trapezoid find: the side if the bases are 6√2 and 4√2, and the acute angle is 45 degrees.

1. A, B, C, D – the tops of the trapezoid. Base ВС = 4√2 cm. Base АD = 6√2 cm. ∠А = 45 °.

BH is the height drawn to the base of AD.

2. We calculate the degree measure ∠АВН:

∠АВН = 180 ° – ∠А – ∠АНВ = 180 ° – 45 ° – 90 ° = 45 °. The AВН triangle is isosceles, since

the angles at the side AB are equal. Therefore, ВН = AН.

3. According to the properties of an isosceles trapezoid AH = (AD – BC) / 2.

AH = (6√2 – 4√2): 2 = √2 cm.

4. AB = √AH² + BH² = √ (√2) ² + (√2) ² = 2 cm.

Answer: the length of the lateral side AB is 2 cm.