Question

The mayor wants you to add a flower bed. The coordinate for the
vertices are:
A(0.5, 0), B(5, 5), C(5, -4), D(-7, -4), E(-7, 5), F(-2.5, 0)

1. Plot the points in alphabetical order to make a polygon. The last
step should be to connect point F to point A.

2. If the distance between point A and point B is 6.7 feet, what is
the perimeter of the flower bed?
Show your work!

3. What is the area of the flower bed?
Show your work!

Answer 1

1. Plot the points in alphabetical order to make a polygon:

A(0.5, 0) --> F(-2.5, 0) --> D(-7, -4) --> E(-7, 5) --> B(5, 5) --> C(5, -4) --> A(0.5, 0)

2. To find the perimeter of the flower bed, we need to calculate the distance between each consecutive pair of points and then sum them up:

Distance between A and F: √( (0.5 - (-2.5))^2 + (0 - 0)^2 ) = √(3^2) = 3
Distance between F and D: √( (-2.5 - (-7))^2 + (0 - (-4))^2 ) = √(4.5^2 + 4^2) = √(20.25 + 16) = √36.25 = 6.02
Distance between D and E: √( (-7 - (-7))^2 + (-4 - 5)^2 ) = √(0^2 + (-9)^2) = √81 = 9
Distance between E and B: √( (-7 - 5)^2 + (5 - 5)^2 ) = √((-12)^2) = 12
Distance between B and C: √( (5 - 5)^2 + (5 - (-4))^2 ) = √(0^2 + 9^2) = √81 = 9
Distance between C and A: √( (5 - 0.5)^2 + (-4 - 0)^2 ) = √(4.5^2 + 4^2) = √(20.25 + 16) = √36.25 = 6.02

Perimeter = 3 + 6.02 + 9 + 12 + 9 + 6.02 = 45.04 feet

3. To find the area of the flower bed, we can split the irregular polygon into a triangle (AFD) and a trapezoid (AFDEB) and calculate the individual areas:

Area of triangle AFD = 0.5 * base * height = 0.5 * 3 * 4 = 6 square feet
Area of trapezoid AFDEB = 0.5 * (sum of parallel sides) * height = 0.5 * (3 + 12) * 4 = 0.5 * 15 * 4 = 30 square feet

Total area = 6 + 30 = 36 square feet.