# The diagonal of an isosceles trapezoid is perpendicular to the lateral side. The height drawn from

The diagonal of an isosceles trapezoid is perpendicular to the lateral side. The height drawn from the top of the obtuse angle divides the base into segments 20 and 5 in length. Find the area of the trapezoid.

1. The tops of the trapezoid – A, B, C, D. AH = 5 cm. DH = 20 cm. BH – height.

2. The length of the segment DH, according to the properties of an isosceles trapezium, is calculated by the formula:

DH = (AD + BC) / 2.

3. Using this formula, we calculate the length of the BC – the smaller base of the trapezoid:

(АD + ВС) / 2 = 20 cm ..

AD = 5 + 20 = 25 cm.

AD + BC = 40 cm ..

BC = 40 – 25 = 15 cm.

4. We calculate the length of the HV height:

BH = √AH x DH = √5 x 20 = √100 = 10 cm.

5. The area of the trapezoid is equal to (AD + BC) / 2 x BH = (25 + 15) / 2 x 10 = 200 cm². 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.