Question

find the area of the polygon with the given vertices.
n(-2, 1), p(3, 1), q(3, -1), r(-2, -1)
the area is \square square units.

Explanation:

Step1: Identify the shape

The vertices are \( N(-2,1) \), \( P(3,1) \), \( Q(3,-1) \), \( R(-2,-1) \). Plotting these points, we see that \( NP \) and \( RQ \) are horizontal lines (same \( y \)-coordinate), and \( N R \) and \( P Q \) are vertical lines (same \( x \)-coordinate). So this is a rectangle.

Step2: Calculate length and width

Length (horizontal side): The distance between \( N(-2,1) \) and \( P(3,1) \) is \( |3 - (-2)| = 5 \) (using distance formula for horizontal line \( d = |x_2 - x_1| \)).

Width (vertical side): The distance between \( P(3,1) \) and \( Q(3,-1) \) is \( |-1 - 1| = 2 \) (using distance formula for vertical line \( d = |y_2 - y_1| \)).

Step3: Calculate area of rectangle

Area of rectangle \( A = \text{length} \times \text{width} \). So \( A = 5 \times 2 = 10 \).

Answer:

10