Part 1: 1. Calculate the perimeter.<span> The perimeter is the combined length of the outline of any two-dimensional figure. For a regular polygon, it can be calculated by multiplying the length of one side by the number of sides
2. </span>Determine the apothem.<span> The apothem of a regular polygon is the shortest distance from the center point to one of the sides, creating a right angle. This is a little trickier to calculate than the perimeter.</span><span>The formula for calculating the length of the apothem is this: the length of the side (s) divided by 2 times the tangent (tan) of 180 degrees divided by the number of sides (n).
3. </span>Know the correct formula.<span> The area of any regular polygon is given by the formula:</span>
<span>Area = (a x p)/2</span>,
<span>where </span>a<span> is the length of the apothem and </span>p<span> is the perimeter of the polygon.
4. </span>Plug the values of a and p in the formula and get the area. As an example, let's use a hexagon (6 sides) with a side (s) length of 10.The perimeter is 6 x 10 (n x s), equal to 60 (so p = 60).The apothem is calculated by its own formula, by plugging in 6 and 10 for n and s. The result of 2tan(180/6) is 1547, and then 10 divided by 1.1547 is equal to 8.66.The area of the polygon is Area = a x p / 2, or 8.66 multiplied by 60 divided by 2. The solution is an area of 259.8 units.Note as well, there are no parenthesis in the "Area" equation, so 8.66 divided by 2 multiplied by 60, will give you the same result, just as 60 divided by 2 multiplied by 8.66 will give you the same result.
Part 2 : 1. Understand that a regular polygon can be thought of as a collection of triangles.<span> Each side represents the base of a triangle, and there are as many triangles in the polygon as there are sides. Each of the triangles are equal in base length, height, and area. </span> 2. Remember the formula for the area of a triangle.<span> The area of any triangle is 1/2 times the length of the base (which, in the polygon, is the length of a side) multiplied by the height (which is the same as the apothem in regular polygon). </span> 3. See the similarities.<span> Again, the formula for a regular polygon is 1/2 times the apothem multiplied by the perimeter. The perimeter is just the length of one side multiplied the by the number of sides (</span>n<span>); for a regular polygon, </span>n<span> also represents the number of triangles that make up the figure. The formula, then, is nothing more than the area of a triangle multiplied by the number of triangles in the polygon.</span>
Volume = Area of a triangle base x height (..or length) Volume = 2,400cm^3 Volume = 1/2(16)(h)(20) 2,400cm^3=1/2(16)(h)(20) 2/400cm^3/160 = 160(h)/160 Part A= 15cm^3=height of the box
PART B
Surface Area = 1/2(15*16)(2)+20(17)(2)+16(20) Surface Area = 240+680+320 Surface Area = 1,240 Part B = You will need approximately 1,240cm of cardboard.
<span>The absolute value of an integer is the numerical valuewithout regard to whether the sign is negative or positive. On a number line it is the distance between the number and zero. Absolute value is also known as magnitude.</span>
