Page 64 - NUMINO Challenge_C2

Basic Concepts Area of Shapes Formed by Connecting Dots

The area of a shape formed by connecting dots on a dotted board can be
found by counting the dots on the perimeter and the dots inside the shape.

The distance between two adjacent dots is 1.
A shape with four dots on the perimeter has an area of 1.

When the number of dots on the perimeter increases
by 1, the area increases by 0.5.

1 1.5 2 2.5

When the number of dots inside the shape increases
by 1, the area increases by 1.

12 3

Therefore, the area of a shape on the dotted board having a distance of 1
between the dots is:
(Number of dots on the perimeter of the shape) 2 (Number of dots inside
the shape) 1.
This equation is called Pick’s Theorem.

Example The distance between adjacent dots is 1. Find the area of colored
shapes A and B.

AB

Class Notes

There are 8 dots on the perimeter of shape A and dots inside the shape.

Using Pick’s Theorem, the area of shape A is 8 2 1 .

There are dots on the perimeter of shape B and dots inside the shape.

Using Pick’s Theorem, the area of shape B is 2 1.

61Geometry