How do I use an area model to explain the product of 4.6 and 3?

Area model is one of a simple step to understand the given situation. So to make it simple, we need to decompose the number.
given number = 4.6 and 3

First we need to get the whole number and start multiplying:
Whole number of 4.6 => 4
whole number of 3 => 3

Now, let’s start multiplying the whole number
=> 4 x 3
=> 12
Then let’s multiply the remaining decimal:
=>.6 x 3
=> 1.8
=> 12 + 1.8
= 13.8

we know that

The area model for multiplication is a pictorial way of representing

multiplication. In the area model, the length and width of a rectangle

represent factors, and the area of the rectangle represents their product

So

in this problem

the factors are

$$length 4.6 \\ wide 3$$

decompose the number $$4.6$$

$$4.6=(4+0.6)$$

$$Area of rectangle=Area rectangle 1+Area rectangle 2\\=(4+0.6)*3\\ =4*3+0.6*3\\ =12+1.8\\ =13.8$$

see the attached figure to better understand the problem

therefore

the product of $$4.6$$ and $$3$$ is equal to $$13.8$$ 