In an isosceles trapezoid, the height forms an angle of 30 ° with the lateral

univerkov | July 20, 2021 | education

In an isosceles trapezoid, the height forms an angle of 30 ° with the lateral side, and the bases are 7 cm and 13 cm. What is the perimeter of the trapezoid?

1. A, B, C, D – the tops of the trapezoid. BE – height to the base of AD. ∠ABE = 30 °. BC = 7 centimeters.

AD = 13 centimeters.

2. According to the properties of an isosceles trapezoid, the segment AE = (AD – BC) / 2 – (13 – 7): 2 = 3 centimeters.

3. AE: AB = sine ∠ABE.

AB = AE: sine 30 ° = 3: 1/2 = 6 centimeters.

4. In an isosceles trapezoid, the sides are equal:

AB = CD = 6 centimeters.

5. The total length of the sides and bases of the trapezoid (perimeter) is equal to AB + CD + BC + AD = 3 + 3 + 7 + 13 = 26 centimeters.

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