An Area Problem

Geometry Level 3

In these shapes, the whole black square the pentagon and circle are inscribed into has the area of $625cm^2$ . In the pentagon diagram, $H$ is the midpoint of $AG$ , $F$ the midpoint of $GE$ , $D$ of $CE$ , $B$ is of $AC$ and finally $A$ is one of the vertices of square $ABCDEFGH$ , as well as the pentagon.

If the area of the circle is $m$ and that of the pentagon is $n$ , then what is $((nm)(n^3-m^2+123.6)/((10^9)(10^4)))$ ?

Round your answer to 3 decimal places

The answer is 1.143.

1 solution

Justin Arun
May 30, 2018

The area of the circle is $156.25pi$ . That of the pentagon is $390.625$ . Insert these into the equation and you would have got a decimal number with the scientific notation of $10$ ^13. You will see that you had to divide by this, so remove the notation, round the result by 3 d.p then you would have got $1.143$ . This was a tricky question, I have to admit. ALSO, THIS IS AN ORIGINAL.

That isn't a square.The square is 625

X X - 3 years ago

Thanks-I changed that

Justin Arun - 3 years ago

I mean the mistake in the problem."If the area of the circle is $m$ and that of the 'square' is $n$ "

X X - 3 years ago

@X X – I changed that too- well done for realising that- it shows how clever you are and saves confusion in the future.

Justin Arun - 3 years ago

An Area Problem

The answer is 1.143.

1 solution

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