Answer:
Area = 18 sq.units
Step-by-step explanation:
Looking at the diagram in the question, one box represents 1 unit.
Thus, the co-ordinates are;
A = (1,4)
B = (4,1)
C = (-2,2)
D = (1,-2)
Now,the vertical component of line BD will be the difference in y values of points B and D.
So, vertical component of Line BD = 1 - (-2) = 1 + 2 = 3
Horizontal component of line BD will be the difference in x values of points B and D
So, horizontal component of line BD = 4 - 1 = 3
So, using Pythagoras theorem;
BD = √3² + 3²
BD = √9 + 9
BD = √18
Now,we are told that the figure is a square. In a square, all sides are equal.
Thus; Area = (BD)² = (√18)² = 18 sq.units
