SOLUTION: What is the area of a square that has a radius of 7(square root of 2) ft (from the center of the square to any vertex)? 49 ft^2 196 ft^2 147 ft^2 196(square root of 2) ft^2

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Question 1141765: What is the area of a square that has a radius of 7(square root of 2) ft (from the center of the square to any vertex)?
49 ft^2
196 ft^2
147 ft^2
196(square root of 2) ft^2
The answer that I got was 49 ft^2. I was not sure how to solve this question, if it's possible to show steps on how it was solved. Thank You!

Found 5 solutions by ikleyn, josgarithmetic, Edwin McCravy, Alan3354, MathTherapy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

If somebody familiar with Math will read it

    "the radius of a square is . . . ", 

he  (or she)  can lose consciousness.



So, be careful when you formulate your thoughts . . . (!)


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Dear Edwin, I saw your notice.

In response, I only can say, that at such education method, the students soon will not be able
to distinct a square from a circle and a diameter from a diagonal.

There is a film / ( a movie)  "Idiocracy"  exactly about such style of life and such style of education / (of teaching).


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Next Alan tries to disprove me and to teach me in his post . . .


Dear colleagues, leave these attempts - I know Geometry from  "a"  to  "Z",  along and across,  in deep and in wide . . .

Regarding terminology,  for regular polygons there are the terms

    "the radius of the inscribed circle"  and  "the radius of the circumscribed circle" 

- and there is  NO  NEED  to invent other / (new) terms to replace / (to substitute) just existing.


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written  by  me.

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OK,  today is the day when I teach  ( = I should teach)  my colleagues - tutors.

In Geometry,  there is no such a term - "radius of a square".


    Only totally illiterate in Geometry can use this term.

    // (Despite of millions links from Google.)


There is the term  "the radius of the circle circumscribed around a square",   INSTEAD.


This is written for tutor  @MathTherapy,  personally.




Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Draw your picture and label all parts.

----------------------------------------------------------------------------
"radius of 7(square root of 2) ft (from the center of the square to any vertex)"
---------------------------------------------------------------------------

There are eight special 45-45-90 triangles; hypotenuse is . You know what to do from here.... right?

x, the side for a leg of one of those triangles; which is also half the length of the side of the original square figure.


You can find the necessary steps from this...

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
If Ikelyn will google "radius of a square" she will find that is is not uncommon
to define "the radius of a square" as the distance from the center of the square
to a vertex.



Draw a vertical line from the center to the right sides:



The right triangle is isosceles and has equal sides, x,



Divide both sides by 2





So the area of the triangle is 





And as we see, the square consists of 8 such triangles:



So the area of the square is 8 times 

Answer  = 196 ft²

Edwin

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Any regular plane figure's dimensions can be specified, and defined by side length, apothem or radius, and the # of sides.
-------
Side length is the length of the sides.
Apothem is the distance from the center to any side.
Radius is the distance from the center to any vertex.
-------------
All of us are wrong sometimes.
It's a statement of facts.
----------------
There's no controversy, and math is not a matter of opinion. We don't vote on it.
The radius of a regular plane figure is the distance from its center to a vertex.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
What is the area of a square that has a radius of 7(square root of 2) ft (from the center of the square to any vertex)?
49 ft^2
196 ft^2
147 ft^2
196(square root of 2) ft^2
The answer that I got was 49 ft^2. I was not sure how to solve this question, if it's possible to show steps on how it was solved. Thank You!
My "TWO CENTS WORTH:" I always associate RADIUS with a CURVE, namely a CIRCLE, but learnt something when Edwin pointed out that the term is also
used to describe a line segment from the center of a square to one of its vertices, and Alan further pointing out that that
describes any line segment from the CENTER of a regular POLYGON to any one of its vertices. The person also points this out.
In this case, and with the polygon being a SQUARE, the radius can also be described as one-half the square's diagonal, in MY OPINION.
You learn something every day! At least I do!
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