In an isosceles trapezoid, the bases are 6 cm and 14 cm, and the lateral side is 5 cm. Find the area of this trapezoid.

univerkov | February 23, 2021 | education

1. A, B, C, D – the tops of the trapezoid. BC = 6 centimeters. AD = 14 centimeters. BE – height.

AB = 5 centimeters. S is the area of the trapezoid.

2. The segment AE of the base AD is calculated by the following formula:

AE = (AD – BC) / 2.

AE = (14 – 6) / 2 = 4 centimeters.

3. We calculate the length of the height BE, for which we apply the Pythagorean theorem:

BE = √AB² – AE² = √5² – 4² = √25 – 16 = √9 = 3 centimeters.

4. S = (AD + BC) / 2 x BE = (14 + 6) / 2 x 3 = 30 centimeters².

Answer: S is equal to 30 centimeters².

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.