Step by step
The question
Question: find the area of the square with corners (2, 1), (5, 1), (5, 4), (2, 4).
square: (2, 1), (5, 1), (5, 4), (2, 4)
1 Plot the points
We put the corners on the grid.
Corner A is (2, 1).
And so on.
We join them in order.
2 Find the side lengths
A B: the same y, so it goes across.
Its length is the bigger x minus the smaller: 5 minus 2 is 3.
= AB: 5 − 2 = 3
B C: the same x, so it goes up and down.
Its length is the bigger y minus the smaller: 4 minus 1 is 3.
= BC: 4 − 1 = 3
3 Area
The area of a square is length times width.
= area = length × width
Careful!
Adding the sides gives the perimeter, the way round.
The area is the squares inside.
Careful: not 3 + 3 + 3 + 3 = 12 ✗
3 times 3 is 9 square units.
= area = 3 × 3 = 9 square units
4 Check
Let's check: count the squares inside.
3 rows of 3 squares: 9.
So the answer is right!
3 rows of 3 squares = 9 squares
Let's look back.
First: plot the points.
Then: find the side lengths.
Then: area.
Last: check.
Answer
= area = 3 × 3 = 9 square units