Calculate the area of a trapezoid with bases of 8 cm and 4 cm and an angle between

Calculate the area of a trapezoid with bases of 8 cm and 4 cm and an angle between the bases and the side of 45 degrees. find the sides of the trapezoid

Since the angle between the base and the sides is the same, the trapezoid is isosceles, AB = СD.

Let’s build the height of the HВ. In an isosceles trapezoid, the BH height divides the larger base into two segments, the length of the smaller of which is equal to the half difference of the base lengths.

AH = (AD – BC) / 2 = (8 – 4) / 2 = 2 cm.

The AVN triangle is rectangular and isosceles, BH = AH = 2 cm.

Then Savsd = (AD + BC) * ВН / 2 = (8 + 4) * 2/2 = 12 cm2.

AB^2 = СD^2 = AH^2 + BH^2 = 4 + 4 = 8.

AB = СD = √8 = 2 * √2 cm.

Answer: The area of the trapezoid is 12 cm2, the sides are 2 * √2 cm.