ABCD is an isosceles trapezoid. Diagonal AC = 10m, CAD angle = 60 degrees. Find S.
| May 7, 2021 | education
Triangles ABD and DCA are equal (AD is common, AB = CD by condition, ∠A = ∠D).
∠CAD = ∠BDA = 60 °.
∠AOD = 180 ° – (60 ° + 60 °) = 60 °. Triangle AOD is equilateral.
∠BCA = ∠DAC = 60 °.
BD = AC = 10 m.
∠BOA = 180 ° – 60 ° = 120 °.
S = ½ AC * BD * sin∠BOA = ½ * 10 * 10 * sin120 ° = 50sin (180 ° – 60 °) = 50sin60 ° = 50 * √3 / 2 = 25√3 ≈ 43.3 (m2).
Answer: S ≈ 43.3 m2.
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