Find the Perimeter of the Polygon with the Given Vertices. Round to the Nearest Hundreth

Question

The given vertices are L(1,4) M(4,0) N(2,0) P(-1,-2)

Answer 1

Use distance formula to calculate lengths of segments between 4 points:

Distance formula = sqrt( (x2-x1)^2 + (y2-y1)^2), where (x1,y1) and (x2,y2) are two consecutive points.

Apply distance formula for (x1,y1) and (x2,y2) = L(1,4) and M(4,0) --> distance is 5

Apply distance formula for (x1,y1) and (x2,y2) = M(4,0) and N(2,0) ---> distance is 2

Apply distance formula for (x1,y1) and (x2,y2) = N(2,0) and P(-1,-2) ---> distance is 3.61

Apply distance formula for (x1,y1) and (x2,y2) = P(-1,-2) and L(1,4) ---> distance is 6.32

Add up all 4 distances to get perimeter = 16.93

Answer 2

Use the distance formula for the distance between points

d = [ ( -1 - 1 )^2 + ( -2 - 4 )^2 ]^(1/2)

d = [ ( 2 - -1)^2 + ( 0 - -2)^ 2 ]^(1/2)

and so for the four pairs

good luck

Answer 3

Just

Compute the distances between consecutive points and sum to get the total distance.

In Matlab:

v = [xcoords,ycoords]; %xcoords and ycoords are column vectors.

n = length(v(:,1));

len_poly = 0;

for i = 1:n-1

len_poly = len_poly + norm(v(i+1,:)-v(i,:),2);

end