Find the perimeter of the polygon with vertices of A(0, 0), B(4, 0) and C(2, 3). Round to the nearest tenth. Just enter one number as your answer.

Help!

sketch it

A to B = 4
A to C = sqrt(2^2 + 3^2) = sqrt(13)
B to C = sqrt(2^2+3^2) = sqrt(13)
so

4 + 2 sqrt (13)

Thank you so much! I'm not good at geometry.

To find the perimeter of a polygon, you need to calculate the sum of the lengths of all its sides. In this case, the polygon has three sides, AB, BC, and CA.

To calculate the length of each side, you can use the distance formula, which is:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the lengths of the sides using the given coordinates:

Length of AB:
(x1, y1) = (0, 0)
(x2, y2) = (4, 0)

DistanceAB = √((4 - 0)^2 + (0 - 0)^2)
DistanceAB = √(16 + 0)
DistanceAB = √16
DistanceAB = 4

Length of BC:
(x1, y1) = (4, 0)
(x2, y2) = (2, 3)

DistanceBC = √((2 - 4)^2 + (3 - 0)^2)
DistanceBC = √((-2)^2 + 3^2)
DistanceBC = √(4 + 9)
DistanceBC = √13

Length of CA:
(x1, y1) = (2, 3)
(x2, y2) = (0, 0)

DistanceCA = √((0 - 2)^2 + (0 - 3)^2)
DistanceCA = √((-2)^2 + (-3)^2)
DistanceCA = √(4 + 9)
DistanceCA = √13

Now, add up the lengths of all the sides to find the perimeter:

Perimeter = DistanceAB + DistanceBC + DistanceCA
Perimeter = 4 + √13 + √13
Perimeter ≈ 4 + 2√13

Rounding to the nearest tenth, the perimeter is approximately 13.6.