Find the perimeter of the polygon with the vertices Q(−3, 2), R(1, 2), S(1,−2), and T(−3,−2).

Question

How do you find the Prerimeter

Answer 1

When you plot the point you will see that you are dealing with a shape that has horizontal lines and vertical lines. Because of that you will not need the distance formula to determine the length of the sides, just count the number of horizontal or vertical units the lines cross over.

The horizontal lines (QR and TS) cover 4 units and the vertical lines (QT and RS) also cover 4 units, so that all 4 sides are 4 units. Thus the perimeter which is the sum of the lengths of all 4 sides is 4 * 4 = 16 square units.

Answer 2

Perimeter is the distance around the shape. To find it, you'll need to find the distance between the points. If you were to graph these points, it would look like:

Q R

T S

so you will need to find the distance between QR, RS, ST, and TQ then add it together.

Distance formula is √(x₂ - x₁)² + (y₂-y₁)²

QR: √(1-(-3)²+ (2-2)^{2 =} √16+0 = √16 = 4

RS: √(1-1)²+ (-2-2)^{2 =} √0 + 16 = √16 = 4

ST: √(-3-1)²+ (-2- (-2))^{2 =} √16+0 = 4

TQ: √(-3-(-3))²+ (2- (-2))^{2 =} √0+16 = 4

All of the sides of a distance of 4, so when you add them together 4 + 4 + 4 + 4 = 16