Find the area of trapezoid circumscribed about a circle?

In summary, The person is seeking help with finding the area of a figure with a circle and a trapezoid. They have tried to create a rectangle inside the trapezoid and find the angle measurements, but are still stuck. They also mention knowing how to find the area of a triangle and the relationship between radius and tangent. The expert suggests breaking up the figure into triangles and using the fact that the radius and tangent are perpendicular at any point on the circle. A hint is also given about two line segments tangent to a circle having the same length if they share a common endpoint.
  • #1
Yuki
5
0
Hello, I have encounted this problem and really need some help =/
The figure is attached. Or you can view it in here: http://img404.imageshack.us/img404/1120/mathhelpppp6yk.gif" [Broken]

Thanks a lot, really urgent :frown:
 

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  • #2
What figures can you compute the area of?
Can you find those figures in this diagram? (Remember, area is additive.)
How would you use information about the circle?
 
  • #3
I have tried to create a rectangle inside that trapezoid, which is from point D and C down to the bottom line. Even though so =s I still can't keep moving =s I note the angle thing on the trapezoid. But like, I also tried to see if I can figure out the degree of Angle CBA or DAB Yet I still get stucked =( I don't know what I am missing to move to next step =/
Thanks for the fast reply
 
  • #4
Can you find the area of a triangle?
Do you know the relationship between a radius and a tangent?
 
  • #5
I know how to find the area of a triangle. However, many triangles can be formed in there =/ So I am kinda lost =s I know radius and tangent, however I never learned any relationship between raidus and tangent
Thanks a lot for help!
 
  • #6
If you can break up your figure into triangles, and you can find the areas of those triangles, then you can add these areas to get the area of the whole figure.

Do you know that at any point on the circle, the radius and tangent-line are perpendicular?
 
  • #7
Here is a hint:

If two line segments share a common endpoint p, and are each tangent to a circle at their opposite endpoints, they have the same length.
 
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1. What is a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides. It is also known as a trapezium in some parts of the world.

2. What does it mean for a trapezoid to be circumscribed about a circle?

Circumscribed means that the trapezoid's vertices lie on the circumference of a circle, with each side of the trapezoid being tangent to the circle.

3. How do you find the area of a trapezoid circumscribed about a circle?

The formula for finding the area of a trapezoid circumscribed about a circle is A = (1/2)h(b1 + b2), where h is the height of the trapezoid and b1 and b2 are the lengths of the two parallel sides.

4. Can you provide an example of finding the area of a trapezoid circumscribed about a circle?

For example, let's say the trapezoid has a height of 10 cm and the two parallel sides have lengths of 6 cm and 12 cm. The area would be A = (1/2)(10)(6 + 12) = 90 cm^2.

5. Why is finding the area of a trapezoid circumscribed about a circle important?

Finding the area of a trapezoid circumscribed about a circle is important in geometry and real-life applications, such as calculating the area of a field or designing a circular swimming pool with a trapezoidal deck. It also helps in understanding the relationship between different shapes and how they can be combined to calculate their areas.

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