Another friend wants a U-shaped flower bed. They want the
coordinate of the vertices to be
A(-7, -4), B(-7, 5), C(-3, 5), D( -3, 0), E(1, 0), F(1, 5), G(5, 5), and H(5, -4)
1. Plot the points on the coordinate grid in alphabetical order and
connect the points to make a U-shaped figure.
2. If the 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. Here is the U-shaped flower bed plotted on the coordinate grid:
A(-7, -4), B(-7, 5), C(-3, 5), D(-3, 0), E(1, 0), F(1, 5), G(5, 5), H(5, -4)
```
H(5, -4) G(5, 5)
F(1, 5) | C(-3, 5)
E(1, 0) D(-3, 0)
A(-7, -4) B(-7, 5)
```
2. To calculate the perimeter of the flower bed, we need to add up the lengths of each side.
Side AB: The distance between A and B is 9 (5 - (-4)).
Side BC: The distance between B and C is 4 (-3 - (-7)).
Side CD: The distance between C and D is 5 (0 - 5).
Side DE: The distance between D and E is 4 (1 - (-3)).
Side EF: The distance between E and F is 5 (5 - 0).
Side FG: The distance between F and G is 4 (5 - 1).
Side GH: The distance between G and H is 9 (5 - (-4)).
Now, add up all the side lengths:
Perimeter = AB + BC + CD + DE + EF + FG + GH
Perimeter = 9 + 4 + 5 + 4 + 5 + 4 + 9
Perimeter = 40 feet
Therefore, the perimeter of the flower bed is 40 feet.
3. To find the area of the flower bed, we can split it into two shapes - a rectangle and a right triangle.
The rectangle has dimensions 4 units by 8 units, so the area of the rectangle is:
Area_rectangle = length * width
Area_rectangle = 4 * 8
Area_rectangle = 32 square feet
The right triangle has base 4 units and height 4 units, so the area of the right triangle is half the area of the rectangle:
Area_triangle = 0.5 * base * height
Area_triangle = 0.5 * 4 * 4
Area_triangle = 8 square feet
Now, add the areas of the rectangle and the triangle together to get the total area of the flower bed:
Total Area = Area_rectangle + Area_triangle
Total Area = 32 + 8
Total Area = 40 square feet
Therefore, the area of the flower bed is 40 square feet.