As shown in the figure, in the isosceles trapezoid ABCD, AB∥CD, diagonal AC⊥BC, ∠ B = 60, BC=2cm, then the area of the trapezoid ABCD is ().

a、33cm2B、6cm2C、6 6cm2D、 12cm2

Test site: the nature of isosceles trapezoid.

Analysis: If the intersection point C is CE⊥ab, and it is known that ∠ CAB = 30, the lengths of AB, AC and CE can be obtained according to the angle of 30 degrees in the right triangle is half of the hypotenuse, and then ∠DAC=∠DCA can be deduced according to the fact that the two angles of the same base of the isosceles trapezoid are equal, so that the length of CD can be obtained.

Answer: solution: the intersection point c is CE⊥AB,

∵AC⊥BC,∠B=60，

∴∠CAB=30，

BC = 2cm，

∴AB=4cm,AC=2 3cm，

∴CE= 3cm，

∵ trapezoid ABCD is an isosceles trapezoid, CD∨AB,

∴∠b=∠dab=60∠cab =∠DCA = 30，

∫∠CAB = 30，

∴∠DAC=∠DCA=30，

∴CD=AD=BC=2cm，

∴ trapezoidal area ABCD =12 (AB+CD) × Ce =12 (4+2) × 3 = 33cm2,

So choose a.

Comments: This question mainly investigates the properties of isosceles trapezoid: ① isosceles trapezoid is an axisymmetric figure, and its symmetry axis is a straight line passing through the midpoint of the upper and lower bottom surfaces;

② The two angles on the same base of isosceles trapezoid are equal;

③ The two diagonals of the isosceles trapezoid are equal.

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