Hello, zillaholic!

Welcome aboard!

i would like to know how to find the area of a circle

in which there is inscribed isosceles trapezoid.

i know the sides of the trapezoid, and i can easily determine the height,

. . Good . . . it is 8, right?

but i don't really see any connection between the circle's radius and the trapezoid.

btw the book says the solution is 157 cm^2.

The diagram looks like this:

Code:

2
D *---* A
/: :\
/ : : \
/ : : \
10 / 8: :8 \ 10
/ : : \
/ : : \
/ : : \
C *-------+-*-+-------* B
: - 6 - : 2 : - 6 - :

Let the center of the circle be

The two segments of the height are: . and

Draw radii

Code:

1 1
D *-*-* A
/ | \
/ | \
/ 8-x| \
10 / | \ 10
/ oP \
/ x| \
/ | \
C *---------*---------* B
: - 7 - E - 7 - :

In the lower right triangle: . .[1]

In the upper right triangle: . .[2]

Equate [1] and [2]: .

Substitute into [1]: .

The area of the circle is:

. .