In a rectangular trapezoid ABCD, the large side is 8 cm, the angle A is 60

In a rectangular trapezoid ABCD, the large side is 8 cm, the angle A is 60 (degrees), and the height BH divides the base of AD in half. Find the area of the trapezoid.

1.∠С = ∠D = 90 °. AB – large lateral side. S is the area of the trapezoid.

2. In a rectangular ΔАВН, the height BH is the leg opposite to ∠A, equal to 60 °, and the AB side of the trapezium is the hypotenuse.

BH / AB = sine 60 ° = √3 / 2.

BH = AB x √3 / 2 = 8 x √3 / 2 = 4√3 cm.

3. AH = √AB² – BH² = √8²- (4√3) ² = √64 – 48 = √16 = 4 cm.

4. АН = DH = 4 cm. АD = 4 + 4 = 8 cm.

5. BC = DH as opposite sides of the BCDN rectangle. BC = 4 cm.

6. S = (AD + BC) / 2 x BH = (8 + 4) / 2 x 4√3 = 24√3 cm².