In rhombus ABCD, all sides = 10 diagonal AC = 5 * (√6 + √3). The angle ABC is 150. Find the S of the rhombus.
| May 9, 2021 | education
The area of a rhombus is calculated by the formula: S = AB * BC * sin (<ABC) = AB * BC * sin (150 °).
<BCA = 180 – <ABC = 180 ° – 150 ° = 30 °. Then S = AB * BC * sin 30 ° = 10 * 10 * 1/2 = 100/2 = 50 (unit2).
The value of the diagonal AC = 5 * (√ 6 + √3) is excessive.
Answer: area S = 50.
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