how do you find the isoperimetric quotient of an n sided figure?
my side lengths are 5cm
i have split it in to triangles so
360/n
is the central angle
then to work out area of singular triangle its 1/2 base times height
height is something like
tan 180/n =2.5 /height length
please help i get stuck here
The sum of the interior angles is (180)(n-2). So each angle in your triangle is half that, divided by n
angle= 90/n * (n-2)
height= 2.5 tan (90/n (n-2))
Put in n, and you have height.
area for the polygon then is n*area of each triangle, where the area of each triangle is 1/2 bh= 1/2 *5*habove.
I need help to answer this question. (n-2)*180=90
If a triangle has a height of 12 in. and a base of 5 in., what is its area?
A. 60 sq. in.
B. 45 sq. in.
C. 30 sq. in.
D. 90 sq. in.
A trapezoid has an area of 33.6 square centimeters and a height of 4 centimeters. What is the sum of the base lengths of the trapezoid?
To find the isoperimetric quotient of an n-sided figure, you need to calculate its perimeter and area. The isoperimetric quotient is then obtained by dividing the square of the perimeter by the area.
Given that the side lengths of your figure are 5 cm and you have split it into triangles, let's break down the steps to find the isoperimetric quotient.
1. Determine the central angle of each triangle:
The sum of the interior angles of any polygon is given by (n-2) * 180 degrees. Therefore, each angle in your triangle is equal to (n-2) * 180 degrees divided by n.
Central angle = (n-2) * 180 / n
2. Calculate the height of each triangle:
You mentioned that the height is related to the tangent function and given by the formula:
height = 2.5 / tan(180/n)
3. Find the area of each triangle:
The area of a triangle is given by multiplying half the base by the height. In this case, the base length is 5 cm, and the height is the value calculated in step 2.
Area of each triangle = (1/2) * 5 * height
4. Determine the total area of the polygon:
To find the total area of the polygon, you need to calculate the area of each individual triangle and then multiply it by the number of triangles (n).
Total area of the polygon = n * Area of each triangle
Now that you have the perimeter (sum of the side lengths) and the area of the polygon, you can calculate the isoperimetric quotient by dividing the square of the perimeter by the area:
Isoperimetric quotient = (Perimeter)^2 / Area
Please note that in order to obtain a numerical value for the isoperimetric quotient, you need to specify the value of n or the number of sides in your figure.