Find the area of an isosceles trapezoid ABCD with a large base AD = 20cm AB = 16cm m (∠A) = 60 °.

Given:

isosceles trapezoid ABCD,

AB = 16 centimeters,

AD = 20 centimeters,

angle A = angle D = 60 degrees.

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

Solution:

1. Consider an isosceles trapezoid ABCD. Let’s draw the heights of HВ and CO. We get the HBCO rectangle. He has ВН = CO.

2. Consider the BHA triangle. Angle AВН = 180 – 90 – 60 = 30 (degrees). So AH = AB: 2 = 16: 2 = 8 centimeters.

3. Right-angled triangle ABН = right-angled triangle COD by hypotenuse and acute angle, since angle A = angle D and CD = AB. Then OD = AH = 8 centimeters.

4. Then BC = 20 – 8 * 2 = 20 – 16 = 4 (centimeters);

5. The area of ​​the trapezium ABCD, that is, S ABCD = 1/2 * (BC + AD) * BH = 1/2 * (4 + 20) * 8 = 4 * 24 = 96 cm ^ 2.

Answer: 96 cm ^ 2.