Question

What is the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​?

Enter your answer in the box. Do not round any side lengths.​

Answer 1

Let’s go through this together :)

First, I plotted the points on a graph (attaches photo).

Now, I am going to count the number of units between each point to find the perimeter.

3 + 8 + 3 + (square root of (4 squared + 3 squared)) + (square root of (4 squared + 3 squared)) = 24

Therefore, the answer is 24 units.

Answer 2

24

Explanation:

when you plot this points, th figure has the form of a house. It is a rectangle with a triangle on top (see attached image)

to know the perimeter wee need the base and height of the rectangle as well as the measure of the size of the sides of the triangle.

By plotting the polygon we see that is has a base of 8, and the rectangle has a height of 3 on each side.

Now to find the sides of the triangle in top we need to use pythagoras, dividing the triangle into 2 identical right triangles we get that these right triangles have sides 3 and 4, so using the Pythagorean theorem for the hypotenuse of the triangle:

`√(4^2+3^2)\\ =√(16+9)\\=√(25)\\ =5`

so the sides of the top triangle measure 5 on each side, and then we sum all quantities to find the perimeter:

3+8+3+5+5 =24