28 How many diagonals are there in a 12-sided convex polygon?

In a 12-sided convex polygon (also known as a dodecagon), we can find the number of diagonals using the formula: \( \frac{n(n - 3)}{2} \), where \( n \) is the number of sides. For a dodecagon, plugging in the values gives us \( \frac{12(12 - 3)}{2} = \frac{12 \times 9}{2} = 54 \). So, there are 54 diagonals in a 12-sided convex polygon! Now, imagine artwork crafted from dodecagons, maybe a stained glass window or a playful geometric design! Diagonals can rightly be the stars in such art! Each diagonal cuts across the polygon, creating smaller shapes, while adding flair to the overall design—bringing mathematics and art together beautifully!