Question

39.
Find the area of a polygon with vertices at (1, 3), (7, 3), (7, 7), and (4, 7).


18 units2


12 units2


10 units2


24 units2

Answer 1

To find the area of the polygon with vertices at \((1, 3)\), \((7, 3)\), \((7, 7)\), and \((4, 7)\), we can break the polygon into two distinct shapes whose areas are easier to calculate: rectangles.

1. **Rectangle 1:**
- Vertices: \((1, 3)\), \((7, 3)\), \((7, 7)\), and \((1, 7)\)
- Length = \(7 - 1 = 6\)
- Width = \(7 - 3 = 4\)
- Area = \(6 \times 4 = 24\) units\(^2\)

2. **Rectangle 2:**
- Vertices: \((4, 7)\), \((7, 7)\), \((7, 4)\), and \((4, 4)\)
- Length = \(7 - 4 = 3\)
- Width = \(7 - 4 = 3\)
- Area = \(\frac{3 \times 3}{2} = 9\) units\(^2\)

Since both shapes are rectangles, the total area is just the area of the larger rectangle minus the overlapping area.

The correct calculation is:
- Length = \(7 - 1 = 6\)
- Width = \(7 - 3 = 4\)
- Area = \(6 \times 4 = 24\) units\(^2\)

So, the area of the polygon is \(\boxed{24 \text{ units}^2}\).