Дано: ABCD, AB║CD, BC ║AD, AB = √13, BC = 6, ∠A = 60 °, S=?
S = a*h, a = BC = 6, h = BK, BK⊥AD
ΔABK - прямоугольный. ∠А = 60°, ∠В = 30° , ⇒AК = √13/2
по т. Пифагора ВК² = 13² - (√13/2)² = 169 - 169/4 = 169*3/4
ВК = h = 13√3/2
S = 6*13√3/2 = 39√3
S = 39√3
Дано: ABCD, AB║CD, BC ║AD, AB = √13, BC = 6, ∠A = 60 °, S=?
S = a*h, a = BC = 6, h = BK, BK⊥AD
ΔABK - прямоугольный. ∠А = 60°, ∠В = 30° , ⇒AК = √13/2
по т. Пифагора ВК² = 13² - (√13/2)² = 169 - 169/4 = 169*3/4
ВК = h = 13√3/2
S = 6*13√3/2 = 39√3
S = 39√3