The perimeter of a square inscribed in a circle is 48 cm. Find the side of a regular pentagon inscribed in this circle.
| May 7, 2021 | education
Find the side of a square as a quarter of its perimeter.
a = 48: 4 = 12 cm.
Let’s use the formula of the sides of a regular polygon (for n = 4) through the radius of the circle described around it and find the radius.
a = 2R * sin180 ° / n.
12 = 2R * sin45 °.
R = 6: 1 / √2 = 6√2 cm.
For a regular pentagon inscribed in the same circle, the same formula is valid, where n = 5.
a = 2 * 6√2 * sin180 ° / 5 = 12√2 * sin45 ° = 12√2 * √ (5 – √5) / 2√2 = 6√ (5 – √5) cm.
Answer: the side of the pentagon is 6√ (5 – √5) cm.
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