Find the area of the rectangle ABCD if AC = 12 cm and makes an angle of 45 degrees with BD.
| September 1, 2021 | education
Data: AC – diagonal length (AC = d = 12 cm); β – acute angle between the considered diagonals (β = 45º).
To find out the area of the specified rectangle ABCD, we will use the formula: S = 0.5 * d2 * sinβ.
Let’s perform the calculation: S = 0.5 * d ^ 2 * sinβ = 0.5 * 12 ^ 2 * sin 45º = 0.5 * 36 * √2 / 2 = 9 * √2 cm2 ≈ 12.73 cm2.
Answer: The area of the specified rectangle ABCD should be 9 * √2 cm2 (12.73 cm2).
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