To calculate the area of a rectangle, we need to determine the lengths of its sides. The vertices given are:
- A (4, 2)
- B (10, 4)
- C (6, 16)
- D (0, 14)
However, it's important to note that the points do not form a rectangle, as we can see from the coordinates. Instead, we can approximate the area by enclosing the points in a rectangle.
Step 1: Find the extreme points
To find an enclosing rectangle, we need to identify the minimum and maximum x and y coordinates from the given points:
- Minimum x (min_x): 0 (from point D)
- Maximum x (max_x): 10 (from point B)
- Minimum y (min_y): 2 (from point A)
- Maximum y (max_y): 16 (from point C)
Step 2: Calculate the width and height of the rectangle
- Width = max_x - min_x = 10 - 0 = 10
- Height = max_y - min_y = 16 - 2 = 14
Step 3: Compute the area of the rectangle
Area = Width × Height = 10 × 14 = 140
Conclusion
The approximate area of the rectangle is 140 square units when rounded to the nearest whole number.
140 units