In trapezoid ABCD, the bases of BC and AD are 2 cm and 8 cm, and the diagonal AC
| May 27, 2021 | education
In trapezoid ABCD, the bases of BC and AD are 2 cm and 8 cm, and the diagonal AC is 4 cm. In what ratio does the diagonal AC divide the area of the trapezoid?
S1 / S2 – the required ratio
Angle BCA = Angle CAD = alpha
S1 = 1/2 * BC * AC * Sin (alpha)
S2 = 1/2 * AC * AD * Sin (alpha)
S1 / S2 = (1/2 * BC * AC * Sin (alpha)) / (1/2 * AC * AD * Sin (alpha))
After all the reductions, we get:
S1 / S2 = 1/2
Answer: The AC diagonal divides the area of the trapezoid ABCD by 2 times.
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