SOLUTION: The apothem of a regular polygon is the perpendicular distance from the center of the polygon to a side. The area, A, of a regular polygon varies jointly as the apothem, a, and the
Algebra.Com
Question 33408: The apothem of a regular polygon is the perpendicular distance from the center of the polygon to a side. The area, A, of a regular polygon varies jointly as the apothem, a, and the perimeter,p. A regular triangle with an apothem of 3 inches and a perimeter of 31.2 inches has an area of 46.8 square inches.
Find the constant variation
Write a joint variation equation
Find the area of a regular triangle with an apothem of 2.3 inches and a perimeter of 12 inches.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
First, you can write:
To find the value of k, the constant of variation, substitute the given values of A, a, and p.
Solve for k.
Divide both sides by 93.6
Constant of variation.
Joint variation equation.
sq.ins.
There is a problem with answer!
If you calculate the area of the given regular (equilateral) triangle using Heron's formula, you will get 6.9 sq.ins. which is just half of what I got using the direct variation method above.
I have concluded that the given apothem (a = 2.3 inches) is just twice what it should be for a regular triangle of 4 inches per side.
You might want to check this out.
RELATED QUESTIONS
Find the perimeter in inches of a regular polygon whose area is 24 square root 3 inches,... (answered by ikleyn)
The perimeter of a regular polygon is 48 and its apothem is 6.What is the area of the... (answered by savvyhush23)
if polygon A and polygon B are similar regular polygons,what will be the measure of the... (answered by ikleyn,ise)
Compute the perpendicular distance from the center to the side of a regular
polygon... (answered by josgarithmetic)
find the side length of a 15-sided regular polygon with apothem a=6 and area A= 282... (answered by Alan3354)
How do you find the area of a regular polygon if you only have the... (answered by shree840)
How do I find the Apothem of a regular polygon? The equation i am trying to use is to... (answered by solver91311)
the number of diagonals of a regular polygon is 56 in.find the perimeter of the polygon... (answered by ikleyn)
The measure of an interior angle of a regular polygon is 144 degrees.find the apothem if... (answered by fractalier)