The middle line of an isosceles trapezoid is 4 m. The angle between the diagonal of the trapezoid and its large

The middle line of an isosceles trapezoid is 4 m. The angle between the diagonal of the trapezoid and its large (lower) base is 30 degrees. Find the area of a trapezoid if its diagonal is 6 m.

Let us lower the height CH from the top of the trapezoid.

Then, in a right-angled triangle ACН, the CH leg lies opposite an angle of 300 and, therefore, its length is equal to half the length of the AC hypotenuse.

CH = AC / 2 = 6/2 = 3 cm.

Since the middle line of the trapezoid is equal to the half-sum of the lengths of the bases of the trapezoid, the area of the trapezoid will be equal to:

Savsd = KР * CH = 4 * 3 = 12 cm2.

Answer: The area of the trapezoid is 12 cm2.