In an isosceles trapezoid, the bases are 5 and 11, and one of the angles between the side

In an isosceles trapezoid, the bases are 5 and 11, and one of the angles between the side and the base is 45 degrees. Find the area of a trapezoid

Given:

Isosceles trapezoid;

Base 1 = 5 units;

Base 2 = 11 units;

Angle = 45 °.

Find: area.

Solution:

Since the trapezoid is isosceles, and the angles between the lateral side and the base are 45 degrees, the heights drawn to the larger base from the corners of the trapezoid cut off the isosceles corners from it. This means that the height of the trapezoid can be calculated:

1) (11 – 5): 2 = 3 (unit).

Now, knowing the height and both bases of the trapezoid, we apply the formula S = 0.5h (a + b) (here h is the height, a and b are the bases):

2) 0.5 * 3 * (11 + 5) = 0.5 * 3 * 16 = 24 (units ^ 2) – the area of the trapezoid.

Answer: 24 units ^ 2.