Question

in the diagram, the side length of each square is 0.1 unit. explain why the area of each square is not 0.1 square units. explain how the diagram shows that the equation (0.4)·(0.2)=0.08 is true. use the drawing tools to help.

Explanation:

First Part: Why the area of each square is not 0.1 square units

Step1: Recall the area formula for a square

The area \( A \) of a square is given by the formula \( A = s \times s \), where \( s \) is the side length of the square.

Step2: Calculate the area of the square

Given that the side length \( s = 0.1 \) unit. Substituting into the formula, we get \( A = 0.1 \times 0.1 \).
Calculating the product: \( 0.1 \times 0.1 = 0.01 \) square units.
Since \( 0.01
eq0.1 \), the area of each square is not 0.1 square units.

Second Part: How the diagram shows \((0.4)\cdot(0.2) = 0.08\) is true

Step1: Analyze the dimensions of the rectangle in the diagram

The length of the rectangle: There are 4 squares along the length, each with side length 0.1 unit. So the length \( l = 4\times0.1 = 0.4 \) units.
The width of the rectangle: There are 2 squares along the width, each with side length 0.1 unit. So the width \( w = 2\times0.1 = 0.2 \) units.

Step2: Calculate the area of the rectangle in two ways

• Way 1: Using length and width

The area \( A \) of a rectangle is \( A = l\times w \). Substituting \( l = 0.4 \) and \( w = 0.2 \), we get \( A=(0.4)\times(0.2) \).

• Way 2: Counting the number of squares

Each square has an area of \( 0.01 \) square units (from the first part). The number of squares in the rectangle: Number of squares along length \( \times \) number of squares along width \( = 4\times2 = 8 \) squares.
So the total area \( A = 8\times0.01 = 0.08 \) square units.

Since both ways of calculating the area of the rectangle give the same result, \( (0.4)\times(0.2)=0.08 \) is true.

Answer:

s:

• For the first part: The area of a square is side length squared. For side length \( 0.1 \), area is \( 0.1\times0.1 = 0.01

eq 0.1 \).

• For the second part: The rectangle has length \( 0.4 \) (4 squares of \( 0.1 \)) and width \( 0.2 \) (2 squares of \( 0.1 \)). Area via length×width: \( 0.4\times0.2 \). Via squares: \( 8\times0.01 = 0.08 \), so \( 0.4\times0.2 = 0.08 \).