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ANSWER

[tex]Area = 196 \: in^{2} [/tex]


EXPLANATION


The area of the smaller square is 4 in².

This means that the smaller square has length,

[tex]l = 2 \: in[/tex]



The scale factor of the dilation is

[tex]k = 7[/tex]
The length of the bigger square becomes,


[tex]L = 7 \times 2 = 14 \: in[/tex]


The area of the dilated square is





[tex]Area=L^2[/tex]

[tex]Area=14^2 = 196 \: in^{2} [/tex]

The correct answer is option D.

The dilation means to magnify or demagnify the object.

The area of the dilated square is 196 in².

What is the square?

It is a type of polygon which having four sides and four vertices. And all the sides and angles are equal.

Area of square = side²

Given

The area of the square is 4 in².

Dilation is 7.

To find

The area of Dilated square.

The area of the square will be

[tex]\begin{aligned} \rm Area\ of\ square\ &= \rm (side)^{2} \\\rm 4 &= \rm (side)^{2} \\\rm side &= 2\\\end{aligned}[/tex]

SIde is dilate by 7 = 2 x 7 = 14 in.

The area of the dilated square will be

[tex]\begin{aligned} \rm Area\ of\ dilated\ square\ &= \rm (side)^{2} \\\\\rm Area\ of\ dilated\ square &= \rm (14)^{2} \\\\\rm Area\ of\ dilated\ square &= 196\\\end{aligned}[/tex]

Thus, the area of the dilated square is 196 in².

More about the square link is given below.

https://brainly.com/question/13747846