Find the area of the parallelogram ABCD if the outside angle at the vertex is B = 45 degrees, AB = 6 cm, BC = 5√3.
| September 1, 2021 | education
Outside angle B and angle A of this parallelogram are crosswise with parallel straight lines BC and AD and secant AB. Therefore, they have the same degree measure, 45 °.
To find the area of the parallelogram, we use the formula:
S = a * b * sin α = AB * AD * sin 45 ° = 6 * 5√3 * √2 / 2 = 15√6 (cm²).
Answer: the area of the parallelogram ABCD is 15√6 cm².
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