Answer :
Let a be the area of smaller pentagon. Then area of the smaller pentagon is a=8 [tex]in^{2}[/tex] .
What is pentagon?
A pentagon is a 2D polygon with five sides and five angles. The word "pentagon" is created by combining the Greek words "penta" (which means "five") and "gon," which means "angles."
Why is pentagon so important?
The President and the Secretary of Defense have exercised global command and control over the nation's armed forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a metaphor for American strength and influence, with all the positive and negative connotations that entails.
Similar figures' surfaces have an area that is proportional to the square of their sides.
The ratio of the sides is on the left, and the ratio of their areas is on the right, therefore we may write this as a proportion.
Keep in mind that the ratio of the sides is squared because we are working with areas.
[tex]\frac{side_{1} ^{2} }{side_{2} ^{2} } =\frac{area_{1} }{area_{2} }[/tex]
Let area a smaller pentagon is a
[tex]\frac{7^{2} }{2^{2} }=\frac{98}{a}[/tex]
a=[tex]\frac{98*4}{49}[/tex]
a= 8 [tex]in^{2}[/tex]
So the area of the smaller pentagon is 8 [tex]in^{2}[/tex]
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