ABCD trapezoid angle d = 30 degrees ad = 25, bc = 15, cd = 8 find the area.

Given:

trapezoid ABCD,

angle D = 30 degrees,

BC = 15 centimeters,

AD = 25 centimeters.

Find the area of the trapezoid ABCD, that is, S ABCD -?

Solution:

1. Consider the trapezoid ABCE. Let’s draw the heights of the CH.

2. Consider the triangle СDН. In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Therefore CH = 1/2 * CD = 1/2 * 8 = 4 centimeters.

3. The area of the trapezium ABCD, that is, S ABCD = 1/2 * (BC + AD) * CH = 1/2 * (15 + 25) * 4 = 2 * 40 = 80 cm ^ 2.

Answer: 80 cm ^ 2.