One garden is regular hexagon shaped. The perimeter of the garden is 1680 m. Posts are put every 10 m along each side, but not at the corners. How many post are needed all together?
The perimeter of a regular hexagon can be calculated by multiplying the length of one side by 6. In this case, the perimeter is 1680 m, so each side of the hexagon is 1680 m / 6 = 280 m.
There are 6 sides in a regular hexagon, so there will be posts every 10 m along each side, except at the corners. Therefore, there will be 280 m / 10 m = 28 posts along each side.
Since there are 6 sides, the total number of posts needed along the sides is 28 posts/side * 6 sides = 168 posts.
However, we also need to consider the corners. There are 6 corners in a regular hexagon, and each corner will need one post. Therefore, we need an additional 6 posts for the corners.
Therefore, the total number of posts needed all together is 168 posts along the sides + 6 posts for the corners = 174 posts.