Math Is Fun Forum

Yumi

Member

Registered: 2006-02-25

Posts: 3

Geometry: Area of Trapezoid Circumscribed About A Circle

Hiii, this is a problem that I have encountered and I need help ASAP.
This is the figure:

Thanks a lot!!

techweb

Member

Registered: 2006-04-09

Posts: 1

Re: Geometry: Area of Trapezoid Circumscribed About A Circle

Perhaps if you find the midsegment of the trapezoid you will have the diameter of the circle which will give you the height of the trapezoid.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,588

Re: Geometry: Area of Trapezoid Circumscribed About A Circle

Area of the trapezium is given by thew formula:-
(Sum of the parallel sides/2)x(distance between them).
Hence, Area=(8+18)/2 x 13= 169 square units.

It can be shown that the diameter of the circle is 13 units.
The two parallel sides of the trapezium are 8 and 18 units respectively.
By constructing triangles on either side of the trapezium, (by dropping perpendiculars from the shorter parallel side to the longer parallel side)and using similarity rules, it can be shown that the middle parallel line, that is, the diameter is wxactly 13 units.
Hence, the area is 169 square units.

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