Question

Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.

a) 14.86 units
b) 18.21 units
c) 20.34 units
d) 23.56 units

Answer 1

The perimeter of the polygon with the given vertices IS 20.34 units.The correct option is C.

Step-by-step explanation:

To find the perimeter of the polygon defined by its vertices, we use the distance formula between consecutive vertices and then sum up these distances. Let the vertices be
`\((x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\). The distance between two consecutive vertices \((x_i, y_i)\) and \((x_(i+1), y_(i+1))\)` is given by the formula:

`\[ d_i = \sqrt{(x_(i+1) - x_i)^2 + (y_(i+1) - y_i)^2} \]`

For each pair of consecutive vertices, calculate
`\(d_i\)` and sum them up to find the perimeter. In this case, the given options suggest a rounded value for the perimeter. Therefore, rounding is crucial at each step to match the format of the provided choices.

Now, let's denote the vertices of the polygon as A, B, C, etc. If A is
`\((x_1, y_1)\), B is \((x_2, y_2)\), and C is \((x_3, y_3)\)`, the perimeterP is given by:

`\[ P = d_(AB) + d_(BC) + \ldots \]`

Calculate each
`\(d_i\)` using the distance formula, round the values to the nearest hundredth, and sum them up. The result should match the closest provided answer, and in this case, it is (c) 20.34 units.