Question

Find the area of a square with the coordinates (-4, 3), (-2, 8), (3, 6), and (1, 1).

Answer 1

Area of the square: 29.0

Step-by-step explanation:

The area of a square is given by

$A=L^2$

where

L is the length of the side of the square

The sides of a square all have the same length, so here we just need to find the length of one side.

The length of the side of the square here is the distance between two vertices, which can be calculated as

$L=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

where

$(x_1,y_1)$  are the coordinates of the 1st vertex

$(x_2,y_2)$ are the coordinates of the 2nd vertex

By taking the two vertices (3,6) and (1,1), we find

$L=\sqrt{(3-1)^2+(6-1)^2}=\sqrt{2^2+5^2}=5.4$

Therefore, the area of the square is:

$A=L^2=5.4^2=29.0$

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