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.
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