Find the area of an isosceles trapezoid with a diagonal of 3√5 and a height of 3.

1. Vertices of the trapezoid – A, B, C, D. Diagonal AC = 3√5 units. Height CH = 3 units. S is the area of the trapezoid.

2. We calculate the segment AH using the formula of the Pythagorean theorem:

AH = √AC² – CH² = √ (3√5) ² – 3² = √45 – 9 = √36 = 6 units.

3. According to the properties of an isosceles trapezoid, the segment AH is calculated by the formula:

AH = (AD + BC) / 2 = 6 units.

4. S = (АD + ВС) / 2 х СН = 6 х 3 = 18 units of measurement².

Answer: S equals 18 units of measurement².