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∠DAO = 45°
Найти: S₀ -?
Высота правильной пирамиды опускается в центр вписанной/описанной окружности ⇒
OA = OB = OC = R - радиус окружности, описанной около ΔABC
ΔAOD - прямоугольный: ∠AOD = 90°; ∠DAO = 45°; DO = 18 см ⇒
∠ADO = 90° - ∠DAO = 90° - 45° = 45° = ∠DAO ⇒
ΔAOD - прямоугольный равнобедренный ⇒
AO = DO = 18 см - радиус описанной окружности R ⇒
AB = BC = AC = a = R√3 = 18√3 см
Площадь равностороннего треугольника
Площадь основания 243√3 см² ≈ 420,9 см²