The side of the trapezoid is 5, and one of the adjacent angles is 30 °. Find the area of a trapezoid

The side of the trapezoid is 5, and one of the adjacent angles is 30 °. Find the area of a trapezoid if its bases are 3 and 9.

1. Draw the height so that it forms a right-angled triangle with the lateral side.
2. Since in a right-angled triangle opposite an angle of 30 ° lies a leg equal to half of the hypotenuse, the height is equal to half of the lateral side. Let’s find it:
h = 5/2 = 2.5 (cm);
3. Let’s write down the formula for the area of a trapezoid:
S = (a + b) / 2 * h, where a and b are bases, h is height.
4. Find the area of the trapezoid:
S = (3 + 9) / 2 * 2.5 = 15 (cm2);
Answer: the area of the trapezium is 15 square centimeters.