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 meters.

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Answer

Calculate area: $A = A B \times B C = 6 \times 9 = 54 ◻$

Steps

Step 1 ：Find lengths of sides of the secret chamber: $A B = \sqrt{(4 - (- 2))^{2} + (- 2 - (- 2))^{2}} = 6$ , $B C = \sqrt{(4 - 4)^{2} + (7 - (- 2))^{2}} = 9$

Step 2 ：Calculate perimeter: $P = A B + B C + C D + D A = 6 + 9 + 6 + 9 = 30$

Step 3 ：Calculate area: $A = A B \times B C = 6 \times 9 = 54 ◻$

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