Question

find the perimeter and area of the rectangle with vertices (5, 2), (-4, 2), (-4, 7), and (5, 7). note that you can draw in the scratch area below, but it is not part of the answer. perimeter: \\(\square\\) units area: \\(\square\\) square units

Explanation:

Step1: Find length and width

For length (horizontal side): Use \( x \)-coordinates of \((5,2)\) and \((-4,2)\). Length \( l = |5 - (-4)| = 9 \).
For width (vertical side): Use \( y \)-coordinates of \((-4,2)\) and \((-4,7)\). Width \( w = |7 - 2| = 5 \).

Step2: Calculate perimeter

Perimeter of rectangle: \( P = 2(l + w) \).
Substitute \( l = 9 \), \( w = 5 \): \( P = 2(9 + 5) = 2(14) = 28 \).

Step3: Calculate area

Area of rectangle: \( A = l \times w \).
Substitute \( l = 9 \), \( w = 5 \): \( A = 9 \times 5 = 45 \).

Answer:

Perimeter: \( 28 \) units
Area: \( 45 \) square units