The Area of a Polygon Slab calculator computes the area of a Polygon (pentagon) slab regular polygon slab with n sides (e.g. n=5 for a pentagon, 6 for a hexagon, 8 for an octagon etc) using the radius (r) from the center of the slab to any one of the vertices (see diagram).
INSTRUCTIONS: Enter the following:
The calculator returns the area in square feet. The default radius units are feet, but the user can choose other length units (e.g. meters) via the pull-down menu. Similarly, the area is returned in square feet, but can be automatically converted to other units (e.g. square meters) via the pull-down menu next to the answer.
This calculation can be used to fit a polygon shaped object (concrete slab, deck, porch, gazebo, etc) in a defined space. Since the polygon whose surface area we are calculating here is defined by a radius to the circle that passes through the vertices of the polygon, you can fit the polygon into any space that will contain that circle of radius r.
So measure an area to have at minimum length and width equal to or greater than the diameter of the circle and the polygon defined by the radius r will fit in this space. And you will know the total area of the polygon space.
Example: A homeowner wishes to put a hexagonal concrete patio slab in a corner of their garden on which they will places some comfortable outside furniture. They want to place the slab centered in a section of the garden where there is a 22 foot by 17 foot open space. They want to make the patio slab as large as possible with its hexagon vertices spanning the center line. And finally, they want to know how many square feet of surface space this hexagon patio provides so they can talk knowledgeably to the supplier of outdoor furniture in making a selection of furniture that will fit comfortably on their new patio.
In the picture to the right, the circle which touches both sides of the rectangular area is the largest circle that would fit in the 22 foot by 17 foot section of the garden. The radius aligned along the center line is half the width of the area: 8.5 feet and the hexagon has number of sides, n = 6.
And thus this equation for the area of a polygon slab tells us the largest slab that will fit the space and be aligned this way will have a surface area:
`"Area"_"Slab"` = 192.15 `ft^2`