Question

what is the perimeter and area of S(0,4), N(3,4), O(3,-4), W(0,-4)

Answer 1

To find the perimeter and area of the quadrilateral defined by the points S(0,4), N(3,4), O(3,-4), and W(0,-4), we can first understand the shape and dimensions of this quadrilateral.

1. **Finding the lengths of the sides**:
- The distance between S(0, 4) and N(3, 4) is:
\[
\text{Distance SN} = \sqrt{(3-0)^2 + (4-4)^2} = \sqrt{3^2} = 3
\]
- The distance between N(3, 4) and O(3, -4) is:
\[
\text{Distance NO} = \sqrt{(3-3)^2 + (-4-4)^2} = \sqrt{(-8)^2} = 8
\]
- The distance between O(3, -4) and W(0, -4) is:
\[
\text{Distance OW} = \sqrt{(0-3)^2 + (-4+4)^2} = \sqrt{(-3)^2} = 3
\]
- The distance between W(0, -4) and S(0, 4) is:
\[
\text{Distance WS} = \sqrt{(0-0)^2 + (4-(-4))^2} = \sqrt{8^2} = 8
\]

2. **Calculating the perimeter**:
The perimeter P of the quadrilateral is the sum of the lengths of all sides:
\[
P = \text{Distance SN} + \text{Distance NO} + \text{Distance OW} + \text{Distance WS} = 3 + 8 + 3 + 8 = 22
\]

3. **Finding the area**:
The quadrilateral formed by these points is a rectangle. The lengths of the sides are:
- Length of SN (or OW) = 3
- Length of WS (or NO) = 8

The area \(A\) of a rectangle is given by:
\[
A = \text{Length} \times \text{Width} = 3 \times 8 = 24
\]

Thus, the perimeter of the quadrilateral is **22** and the area is **24**.