(A coordinate plane)
One friend wants an L-shaped flower bed. They want the
coordinates for the vertices to be:
A (-2, -4), B (-2, 6), C (0, 6), D (0, -2), E (3, -2), and F (3, -4)
1. Plot the points on the coordinates grid in alphabetical order and
connect the points to make an L-shaped figure
2. If length is measured in feet, what is the perimeter of the flower bed?
Show your work!
3. What is the area of the flower bed?
Show your work!
1. The L-shaped flower bed plotted on the coordinate plane:
A (-2, -4)
F (-2, 6) E (3, -2)
D (-2, 6) C (0, 6)
B (0, -2)
2. To find the perimeter of the flower bed, we need to calculate the distances between each pair of consecutive points and then add them up.
Distance between A and B:
√((-2-0)^2 + (-4-(-2))^2) = √(4 + 4) = √8 = 2√2
Distance between B and C:
√((0-0)^2 + (-2-6)^2) = √(64) = 8
Distance between C and D:
√((0-(-2))^2 + (6-6)^2) = √(4) = 2
Distance between D and E:
√((-2-3)^2 + (6-(-2))^2) = √(25 + 64) = √89
Distance between E and F:
√((3-(-2))^2 + (-2-(-4))^2) = √(25 + 4) = √29
Perimeter = 2√2 + 8 + 2 + √89 + √29
Perimeter ≈ 2.83 + 8 + 2 + 9.43 + 5.39
Perimeter ≈ 27.65 feet
3. To find the area of the flower bed, we need to divide it into rectangles and a triangle.
Area of rectangle ABDC:
Length = 6 units, Width = 2 units
Area = 6*2 = 12 square units
Area of rectangle CEDF:
Length = 3 units, Width = 4 units
Area = 3*4 = 12 square units
Area of triangle BDE:
Base = 3 units, Height = 6 units
Area = 0.5*3*6 = 9 square units
Total Area = 12 + 12 + 9 = 33 square units
Therefore, the area of the L-shaped flower bed is 33 square units.