Christmas Present plotted on a coordinate grid.

- The image displays a Christmas present on a coordinate plane.
- The task is to find the area of the red bow on the present.
- The bow is composed of several geometric shapes: two large loops, a central knot, and two triangular tails.
- To calculate the total area, we can break the bow down into these simpler shapes, calculate their individual areas, and sum them up.

Step 1: Calculate the area of one large loop.
- The left loop can be approximated as a polygon with vertices at approximately (-10, 12), (-8, 14), (-6, 13), (-5, 11), (-7, 9), (-10, 9).
- Using the Shoelace formula for the polygon with vertices (x₁,y₁), (x₂,y₂), ..., (xₙ,yₙ):
Area = ½ |Σ(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|
For the left loop:
Vertices in order: (-10,12), (-8,14), (-6,13), (-5,11), (-7,9), (-10,9), and back to (-10,12).
Calculating:
(-10)(14) + (-8)(13) + (-6)(11) + (-5)(9) + (-7)(9) + (-10)(12) = -140 - 104 - 66 - 45 - 63 - 120 = -498
(12)(-8) + (14)(-6) + (13)(-5) + (11)(-7) + (9)(-10) + (9)(-10) = -96 - 84 - 65 - 77 - 90 - 90 = -402
Area = ½ |-498 - (-402)| = ½ |-96| = 48 square units.
- The right loop is symmetric, so its area is also 48 square units.
- Total area for both loops: 48 + 48 = 96 square units.

Step 2: Calculate the area of the central knot.
- The central knot is a rectangle with vertices at approximately (-3, 8), (3, 8), (3, 10), (-3, 10).
- Width = 3 - (-3) = 6 units.
- Height = 10 - 8 = 2 units.
- Area = 6 * 2 = 12 square units.

Step 3: Calculate the area of the two triangular tails.
- The left tail is a triangle with vertices at approximately (-3, 0), (-5, -3), (-1, -3).
- Base = distance between (-5,-3) and (-1,-3) = 4 units.
- Height = vertical distance from (-3,0) to the base y=-3 = 3 units.
- Area = ½ * base * height = ½ * 4 * 3 = 6 square units.
- The right tail is a triangle with vertices at approximately (3, 0), (5, -3), (1, -3).
- Base = distance between (1,-3) and (5,-3) = 4 units.
- Height = vertical distance from (3,0) to the base y=-3 = 3 units.
- Area = ½ * 4 * 3 = 6 square units.
- Total area for both tails: 6 + 6 = 12 square units.

Step 4: Sum all areas.
- Total area of the bow = Area of loops + Area of knot + Area of tails
- Total area = 96 + 12 + 12 = 120 square units.

The area of the red bow is 120 square units.