Answer:
Perimeter = 24 units
Area = 36 square units
Explanation:
An archaeologist divides an area using a coordinate plane in which the coordinates are measured in meters. The vertices of a secret chamber are (-4,-1), (2,-1) , (2,5) , and (-4,5) . Find the perimeter and the area of the secret chamber.
We have to find the length of the sides of the rectangle using the formula below
= √(x2 - x1)² + (y2 - y1)² when given vertices (x1, y1) and (x2, y2)
For sides A
(-4,-1), (2,-1)
= √(2 - (-4))² + (-1 -(-1))²
= √(2 + 4)² + (0)²
= √6²
= √36
= 6 units
Side B
(2, -1), (2,5)
= √(2 - 2)² + (5 - (-1))²
= √0² + (5 + 1)²
= √0 + 6²
= √36
= 6 units
For side C
(2,5) , and (-4,5)
= √(2 - (-4))² + (5 - 5)²
= √6² + 0²
= √36
= 6 units
For side d
(-4,-1), (-4,5)
= √(-4 - (-4))² + (5 - (-1))²
= √(-4 +4)² + (5 + 1)²
= √0 + 6²
= √36
= 6 units
From the above calculation, all the sides of the secret chamber are equal to one another
Side a = Side b = Side c = Side d
This means the chamber is has the shape of a square.
The perimeter of the secret chamber =
P = 4a
a = Length of one side = 6 units
P = 4 × 6 units
P = 24 units
The area of the secret chamber
A = a²
a = Length of one side = 6 units
A = ( 6 units)²
P = 36 square units