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!
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!
Answers
GPT 3.5
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.
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.