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Q: What is the area of a polygon with a perimeter of 10 ft and an apothem of 2 ft?

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Such a polygon is not possible.

10 square feet

Area of regular polygon: 0.5*2*10 = 10 square feet

The answer will depend on the number of sides in the polygon. Since that information is not given, there can be no answer.

Area of a regular polygon equals to the one half of the product of its perimeter with the apothem. So we have: A = (1/2)(a)(P) Since our polygon has 10 sides each with length 1.2, the perimeter is 12 910 x 1.2). Substitute 12 for the perimeter, and 1.85 for the apothem in the area formula: A = (1/2)(a)(P) A = (1/2)(1.85)(12) A = 11.1 Thus, the area of the decagon is 11.1.

Even if you knew how many sides the polygon has, you stillcould not calculate its perimeter with that much information.Examples:-- An equilateral triangle with area of 20 has perimeter of 20.3885 .-- A square with area of 20 has perimeter of 17.889(rounded).-- A rectangle with area of 20 can have any perimeter more than 17.889 .4 by 5 . . . . area = 20, perimeter = 182 by 10 . . . area = 20, perimeter = 241 by 20 . . . area = 20, perimeter = 42..etc.

The area of square is : 100.0

The answer will depend on what measure you are interested in: interior or exterior angles, lengths of sides, principal diagonals, apothem, area.

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50

An apothem is the red segment in the diagram (Figure1). B is the center point of the hexagon, and the blue line are radii of the polygon. An apothem is always from the center of the polygon, to the outside, and it is always perpandicular to the side it is touching. You find the area of any polygonwith this equation: (.5) n a s In the formula, n= number of sides, a= the length of the apothem, and s= the length of any given side. Figure1: seehttp://education.yahoo.com/homework_help/math_help/solutionimages/minigeogt/10/1/1/minigeogt_10_1_1_14_90/f-548-17-1.gifHope I helped!!!

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