Problem
An archaeologist divides an area using a coordinate plane in which the coordinates are measured in meters. The vertices of a secret chamber are \( (-2,-2),(4,-2),(4,7) \), and \( (-2,7) \). Find the perimeter and the area of the secret chamber. The perimeter of the secret chamber is meters, and the area is \( \square \) square meters.
Solution
Step 1 ：Find lengths of sides of the secret chamber: \(AB = \sqrt{(4 - (-2))^2 + (-2 - (-2))^2} = 6\), \(BC = \sqrt{(4 - 4)^2 + (7 - (-2))^2} = 9\)
Step 2 ：Calculate perimeter: \(P = AB + BC + CD + DA = 6 + 9 + 6 + 9 = 30\)
Step 3 ：Calculate area: \(A = AB \times BC = 6 \times 9 = 54\square\)
