Area of triangle with corners (2, 4), (7, 4), (4, 1)

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 (2, 4), (7, 4), (4, 1).

triangle: (2, 4), (7, 4), (4, 1)

We put the corners on the grid.

Corner A is (2, 4).

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: 7 minus 2 is 5.

= base AB: 7 − 2 = 5

The height goes straight up from C to the base line.

It goes from y = 1 to y = 4: 3 units.

= height: 4 − 1 = 3

The area of a triangle is a half times base times height.

= area = 12 × base × height

Careful!

Base times height is the whole rectangle around it.

The triangle is half of that.

Careful: not 5 × 3 = 15 ✗

Half of 5 times 3 is 7.5 square units.

= area = 12 × 5 × 3 = 7.5 square units

Let's check: the rectangle around the base and the height is 5 by 3: 15 squares.

The triangle takes half of it: 7.5.

So the answer is right!

rectangle 5 × 3 = 15, half = 7.5

Let's look back.

First: plot the points.

Then: find the base and height.

Then: area.

Last: check.

Answer

= area = 12 × 5 × 3 = 7.5 square units

Try this one yourself, then check:

triangle: (1, 6), (6, 6), (3, 3)

Show the answer

7.5 square units