Area of triangle with corners (1, 1), (5, 1), (1, 6)

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 (1, 1), (5, 1), (1, 6).

triangle: (1, 1), (5, 1), (1, 6)

We put the corners on the grid.

Corner A is (1, 1).

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: 5 minus 1 is 4.

= base AB: 5 − 1 = 4

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

It goes from y = 6 to y = 1: 5 units.

= height: 6 − 1 = 5

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 4 × 5 = 20 ✗

Half of 4 times 5 is 10 square units.

= area = 12 × 4 × 5 = 10 square units

Let's check: the rectangle around the base and the height is 4 by 5: 20 squares.

The triangle takes half of it: 10.

So the answer is right!

rectangle 4 × 5 = 20, half = 10

Let's look back.

First: plot the points.

Then: find the base and height.

Then: area.

Last: check.

Answer

= area = 12 × 4 × 5 = 10 square units

Try this one yourself, then check:

triangle: (0, 0), (4, 0), (0, 4)

Show the answer

8 square units