The bases of an isosceles trapezoid are 5 and 13 and the tangent of the angle at one of the bases is 3/4 find its area.

To find the area of a trapezoid, we need to find its height. We lower the height from the top-end of the smaller base to the larger base.

It forms a right-angled triangle, in which the legs are the height of the trapezoid and the difference between the bases of the trapezoid, divided by two. The tangent of the angle at the base of the trapezoid will be:

tg A = h / ((b – a) / 2);

tg A = 2 * h / (b – a);

h = tg A * (b – a) / 2 = 3/4 * (13 – 5) / 2 = 3/8 * 8 = 3;

Then the area is equal to:

S = (a + b) * h / 2 = (5 + 13) * 3/2 = 9 * 3 = 27.