Worked examples
The question
Question: find the area of the rectangle with corners (1, 1), (5, 1), (5, 4), (1, 4).
rectangle: (1, 1), (5, 1), (5, 4), (1, 4)
1 Plot the points
We put the corners on the grid.
Corner A is (1, 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 1 is 4.
= AB: 5 − 1 = 4
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 rectangle 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 4 + 3 + 4 + 3 = 14 ✗
4 times 3 is 12 square units.
= area = 4 × 3 = 12 square units
4 Check
Let's check: count the squares inside.
3 rows of 4 squares: 12.
So the answer is right!
3 rows of 4 squares = 12 squares
Let's look back.
First: plot the points.
Then: find the side lengths.
Then: area.
Last: check.
Answer = area = 4 × 3 = 12 square units
▶ Watch it solved
The question
Question: find the perimeter of the rectangle with corners (−2, −1), (3, −1), (3, 2), (−2, 2).
rectangle: (−2, −1), (3, −1), (3, 2), (−2, 2)
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: 3 minus −2 is 5.
= AB: 3 − (−2) = 5
Careful!
−2 is on the other side of 0.
Minus a negative is plus: 3 plus 2.
Careful: not 3 − 2 = 1 ✗
B C: the same x, so it goes up and down.
Its length is the bigger y minus the smaller: 2 minus −1 is 3.
= BC: 2 − (−1) = 3
3 Perimeter
The perimeter is the way round: all four sides.
= perimeter = all four sides
5 plus 3 plus 5 plus 3 is 16 units.
= perimeter = 5 + 3 + 5 + 3 = 16 units
4 Check
Let's check: opposite sides are the same.
So it is 2 times 5 plus 3: 2 times 8 is 16.
So the answer is right!
2 × (5 + 3) = 2 × 8 = 16
Let's look back.
First: plot the points.
Then: find the side lengths.
Then: perimeter.
Last: check.
Answer = perimeter = 5 + 3 + 5 + 3 = 16 units
▶ Watch it solved
The question
Question: find the area of the triangle with corners (−3, −2), (3, −2), (0, 3).
triangle: (−3, −2), (3, −2), (0, 3)
1 Plot the points
We put the corners on the grid.
Corner A is (−3, −2).
And so on.
We join them in order.
2 Find the base and height
base A B: the same y, so it goes across.
Its length is the bigger x minus the smaller: 3 minus −3 is 6.
= base AB: 3 − (−3) = 6
Careful!
−3 is on the other side of 0.
Minus a negative is plus: 3 plus 3.
Careful: not 3 − 3 = 0 ✗
The height goes straight down from C to the base line.
It goes from y = 3 to y = −2: 5 units.
= height: 3 − (−2) = 5
3 Area
The area of a triangle is a half times base times height.
= area = 12 × base × height
Half of 6 times 5 is 15 square units.
= area = 12 × 6 × 5 = 15 square units
4 Check
Let's check: the rectangle around the base and the height is 6 by 5: 30 squares.
The triangle takes half of it: 15.
So the answer is right!
rectangle 6 × 5 = 30, half = 15
Let's look back.
First: plot the points.
Then: find the base and height.
Then: area.
Last: check.
Answer = area = 12 × 6 × 5 = 15 square units
▶ Watch it solved
