Step by step
The question
Question: find the area of the triangle with corners (−2, 0), (4, 0), (1, 5).
triangle: (−2, 0), (4, 0), (1, 5)
1 Plot the points
We put the corners on the grid.
Corner A is (−2, 0).
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: 4 minus −2 is 6.
= base AB: 4 − (−2) = 6
Careful!
−2 is on the other side of 0.
Minus a negative is plus: 4 plus 2.
Careful: not 4 − 2 = 2 ✗
The height goes straight down from C to the base line.
It goes from y = 5 to y = 0: 5 units.
= height: 5 − 0 = 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