Find the area of a rectangular trapezoid, the bases of which are 5 cm and 17 cm

Find the area of a rectangular trapezoid, the bases of which are 5 cm and 17 cm, the large side side is 10 cm, and the smaller angle is 30 degrees.

1. S – Area of the trapezium ABCD. ∠А = ∠В = 90 °. ∠D = 30 °. CE – height. BC = 5 centimeters. AD = 17 centimeters. CD = 10 centimeters.

2. We calculate the length of the height BE through one of the trigonometric functions ∠D – sine ∠D:

CE / CD = sine ∠D = sine 30 ° = 1/2.

CE = CD x 1/2 = 10 x 1/2 = 5 centimeters.

3. S = (AD + BC) / 2 x CE = (17 + 5) / 2 x 5 = 55 centimeters².

Answer: S equals 55 centimeters².