The diagonal of an isosceles trapezoid is perpendicular to the side. Find the area of the trapezoid

The diagonal of an isosceles trapezoid is perpendicular to the side. Find the area of the trapezoid if its bases are 7 and 25 cm

1. The tops of the trapezoid – A, B, C, D. BC = 7 cm. AD = 25 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 = (25 + 7) / 2 = 16 cm.

3. Segment АН = АD – DH = 25 – 16 = 9 cm.

4. The length of the BH height drawn from the top of the right angle is calculated by the formula:

BH = √AН x DH = √9 x 16 = 12 cm.

5. Area of the trapezoid = (AD + BC) / 2 x BH = (25 + 7) / 2 x 12 = 16 x 12 = 192 cm².

Answer: the area of the trapezoid is 192 cm².