Area of triangle with corners (-3, -2), (3, -2), (0, 3)

Step by step, with the reason for every step · Polygons on the grid · Algebra 1

Step by step

Question: find the area of the triangle with corners (−3, −2), (3, −2), (0, 3).

triangle: (−3, −2), (3, −2), (0, 3)

We put the corners on the grid.

Corner A is (−3, −2).

And so on.

We join them in order.

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

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

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

Try this one yourself, then check:

triangle: (−4, −1), (3, −1), (0, 5)

Show the answer

21 square units