How to Describe a Shape in Terms of Its Area and Perimeter

Shapes are a fundamental component of geometry.
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Points, lines and shapes are the fundamental components of geometry. Every shape, except for a circle, is composed of lines that intersect at a vertex to create a boundary. Each shape has a perimeter and area. Perimeter is the distance around the edge of a shape. Area is the amount of space within a shape. Both of these parameters can be made into equation form to describe the shape in specific terms.

    Determine if the shape is a circle. The perimeter of a circle is the diameter multiplied by pi, or pi_D. The area of a circle is the radius squared multiplied by pi, or pi_r^2.

    Determine if the shape is a square. The perimeter of a square is four times the length of one side, or 4*l. The area of a square is the length squared, or l^2.

    Determine if the shape is a triangle. For an equilateral triangle, in which all sides are equal, the perimeter is three times the length of one side, or 3_l. For any other triangle, the perimeter is l1+l2+l3, where each "l" variable is a side of the triangle. The area of a triangle is half its base times its height, or (1/2)_b*h.

    Determine if the shape is a rectangle. The perimeter of a rectangle is twice the length plus twice the width, or 2_w + 2_l. The area of a rectangle is the length times the width, or l*w.

    Determine if the shape is a regular polygon. A regular polygon has angles and sides of identical sizes. The perimeter of a polygon is n_l, where "n" is the number of sides and "l" is the length of a side. The area of a regular polygon is (l^2_n)/[4*tan(pi/n)] where "l" is the length of a side and "n" is the number of sides.

    Determine if the shape is an irregular polygon. The perimeter of an irregular polygon is l1+l2+l3+...+ln, where each "l" variable is the length of a side and "ln" is the length of the last, or "nth," side. There are multiple ways to find the area of an irregular polygon. The most common way is to break the shape up into more easily describable shapes. For example, if the irregular polygon is in the shape of a house, then break the shape up into a square with a triangle on top. In this case, the area would be l^2+(1/2) b*h.

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