geometry: find the area of the trapezium

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Natasha

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A circle of circumference 12cm is inscribed in a square which in turn is inscribed in an outer circle. This outer circle touches the parallel sides of a trapezium as shown. Find the area of the trapezium, giving your answer in the form (a sqrt(b))/pi

IMAG0926.jpg

(My first post! Genuinely unsure how to start this question, let alone finish it. Some prompting would be helpful. Also, in case the mathematical form of the answer is confusing, I mean :
a square root b all over pi
Thanks!)
 
Denis said:
To start: get radius of the 12cm circle

Hint: the height of the trapezium = circumference of larger circle

Would you be able to solve if the trapezium height was given?
Click to expand...

Were you missing the corner so much that you got confused between the diameter and the circumference?!!!
 
Natasha said:
A circle of circumference 12cm is inscribed in a square which in turn is inscribed in an outer circle. This outer circle touches the parallel sides of a trapezium as shown. Find the area of the trapezium, giving your answer in the form (a sqrt(b))/pi

attachment.php


(My first post! Genuinely unsure how to start this question, let alone finish it. Some prompting would be helpful. Also, in case the mathematical form of the answer is confusing, I mean :
a square root b all over pi
Thanks!)
Click to expand...

Start with the radius of the inside circle. Since the circumference is 12cm, the radius rI is given by
rI = 12/(2\(\displaystyle \pi\)) = 6/\(\displaystyle \pi\)
Now what is the side length of the square (in terms of rI)
sS = ?
The radius of the outside circle (convert to in terms of rI)
rO = ?
The height of the trapezium [BTW, in the US & Canada it is called a trapezoid] (convert to in terms of rI)
hT = ?
(Hint: think of an outside square]
Now, with the given lengths of 2cm for the top and 5cm for the bottom, you should have enough information.
 
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