Step by step
The question
Question: find the area of the triangle with corners (0, 3), (5, 3), (2, −1).
triangle: (0, 3), (5, 3), (2, −1)
1 Plot the points
We put the corners on the grid.
Corner A is (0, 3).
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: 5 minus 0 is 5.
= base AB: 5 − 0 = 5
The height goes straight up from C to the base line.
It goes from y = −1 to y = 3: 4 units.
= height: 3 − (−1) = 4
Careful!
−1 is on the other side of 0.
Minus a negative is plus.
Careful: not 3 − 1 = 2 ✗
3 Area
The area of a triangle is a half times base times height.
= area = 12 × base × height
Half of 5 times 4 is 10 square units.
= area = 12 × 5 × 4 = 10 square units
4 Check
Let's check: the rectangle around the base and the height is 5 by 4: 20 squares.
The triangle takes half of it: 10.
So the answer is right!
rectangle 5 × 4 = 20, half = 10
Let's look back.
First: plot the points.
Then: find the base and height.
Then: area.
Last: check.
Answer
= area = 12 × 5 × 4 = 10 square units