Find the perimeter of ABCD

Question

Find the perimeter of the polygon formed with these points are connected;

A (3,4)

B (3,1)

C (8,1)

D (8,4)

Perimeter = ___ units

Answer 1

Hi,

Coordinates were given, 4 points on a coordinate graph.

Steps:

1. Graph the 4 points on the graph.

(Please make sure that all points are labeled with the coordinates and the letter names.)

1. Q: What kind of figure d o you have ?

Answer: This polygon is a rectangle. The rectangle is called rectangle ABCD.

Characteristics are important here:

Opposite sides are equal.

The rectangle has four 90 degree angles (right angles)

3. Find the lengths of segment AB by simply adding the units from point A to point B. AB=length of AB=3 units

4. Now find length of segment BC=5 units. Just count from points B to point C.

Note: BC= AD=5. And AB=DC=3

(Distance from B to C is equal to the distance from A to D, and the distance from A to B is equal to the distance from D to C).

Q: What are you asked to do?

A: Find the perimeter of the polygon.

Q: What is perimeter?

A: Perimeter is the distance around the rectangle.

You can add all the distances around, or you can use the following formula: P= 2(l) + 2 (w).

The perimeter is equal to twice the length plus twice the width.

Answer 2

In reviewing the question, we were given coordinates.

1. Construct your Cartesian plane on graph paper.
2. Plot the points on the cartesian plane and this will be seen as a rectangle (Polygon) after each point has been connected.
3. Count the UNIT between each point to find out what the distance is between each Vertex.
4. Distance between AB would be 5 units and the distance DC would be 3 units.
5. In a rectangle opposite sides equal, and as such AB (5 units) = CD (5 units) and AC (3 units) = AD (3 units).
6. Perimeter means distance around an object; To find the perimeter of the rectangle, add all the lengths of the rectangle (AB+BC+CD+DA).

The perimeter of the rectangle would be:

5+3+5+3 = 16 units

Answer 3

You can use the distance formula to solve this. Distance = Square root of (x₂ - x₁) + (y₂ - y₁)

From A to B, (3 - 3)² + (1 - 4)² = 0² + (-3)² = 0 + 9 = 9. Square root of 9 = 3

From B to C, (8 - 3)² + (1 - 1)² = 5² + 0² = 25 + 0 = 25. Square root of 25 = 5

From C to D, (8 - 8)² + (4 - 1)² = 0² + 3² = 0 + 9 = 9. Square root of 9 = 3

From D to A, (3 - 8)² + (4 - 4)² = (-5)² + 0² = 25 + 0 = 25. Square root of 25 = 5.

Now add all side lengths together: 3 + 5 + 3 + 5 = 16

Perimeter = 16