Question

Square ABCD is shown on the graph. What is the area of the square?

Answer 1

Area = 18 sq.units

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