Question

Find the perimeter of the polygon defined by the coordinates (3, 10), (10, 0), (-1, -2), and (-3, 10). (Round to nearest tenth)

Answer 1

Answer:

Perimeter = 100units

Step-by-step explanation:

To answer the question, firstly some concepts to be revised:

Polygon:

Any geometry having any number of sides.

Perimeter:

The sum of the lengths of all the sides of any polygon.

Now, as we are given 4 points; namely:

A(3,10), B(10,0), C(-1,-2) and D(-3,10)

Now, to compute the perimeter, we must know the lengths of all the sides. And for that, we can simply use distance formula to calculate distance between any two points as:

d = √(x1-x2)²+(y1-y2)² --(i)

having,

'(x1,y1)' and '(x2,y2)' as the coordinates of the given points.

Now, as mentioned the definition of polygon, the value of it can be obtained by summing up all the lengths of the sides, so;

Perimeter = P = AD + AB + BC + CD

Where;

AB, BD, AC, and CD shows the distances between each pair of points.

Now, to compute distances;

For AB:

AB = √(3-10)²+(10-0)²

Thus,

AB = √(7²+10²)

AB = √149 units

For AD:

AD = √(3-(-3))²+(10-10)²

AD = √(6²+0²)

AD = 6 units.

For BC:

BC = √(10-(-1))²+(0-(-2))²

BC = √(11²+2²)

BC = √125 units

For DC:

DC = √(-3-(-1))²+(10-(-2))²

DC = √(2²+12²)

DC = √148 units

Now, for perimeter, summing up all the lengths as;

P = 6 +√149 +√ 125 + √148

P = 96.58 units.

And to round it off to the nearest tenth;

P = 100 units.