Can you find the area of a trapezoid with four given side lengths?

In summary, the area of a trapezoid can be found by using the formula A=5*SQRT(32/9)/2 or simplified to 10SQRT(2)/3. The parallel sides must be 1 and 4, and the height can be calculated using the triangle inequality. Both solutions presented by the conversation participants result in the same answer of 10SQRT(2)/3.
  • #1
Albert1
1,221
0
1,2,3,4 are four side length of a trapezoid,please find the area of

this trapezoid
 
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  • #2
Re: the area of a trapezoid

Parallel sides must be 1 and 4.

Area = 5*SQRT(32/9) / 2 = ~4.714
 
  • #3
Re: the area of a trapezoid

yes, your answer is correct =$\dfrac {10\sqrt 2}{3}$ :cool:

can you show your detailed solution please ?
 
  • #4
Re: the area of a trapezoid

We don't do homework here (Sun)

OK; of the 6 possibilities, only 1:4 is possible as parallels;
can be easily shown using triangle inequality. Good nuff?
Code:
         A     1     B

     2                         3
    

D  3-e   F     1     E          e           C
Let height AF = BE = h, and EC = e; then:
triangleADF: h^2 = 2^2 - (3 - e)^2
triangleBCE: h^2 = 3^2 - e^2

SO:
2^2 - (3 - e)^2 = 3^2 - e^2
solve: e = 7/3
so DF = 2/3 and h = (4/3)SQRT(2)

Leads to area = 5*SQRT(32/9) / 2
which may be simplified to 10SQRT(2) / 3.
 
  • #5
Re: the area of a trapezoid

This is not my homework ,at first you must decide how to plot this trapezoid(this part may be a challenge)
here is my solution :
View attachment 1118
$h^2=9-x^2---(1)$
$h^2=4-(3-x)^2---(2)$
from (1)(2) we get $x=\dfrac {7}{3},\,\, and ,\,\, h=\dfrac {4\sqrt 2}{3}$
$\therefore area=2.5h=\dfrac {10\sqrt 2}{3}$
 

Attachments

  • trapezoid.jpg
    trapezoid.jpg
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  • #6
Re: the area of a trapezoid

Albert said:
This is not my homework...
I know that, Albert; I was making a joke :cool:

I see no difference between your solution and mine.
 

FAQ: Can you find the area of a trapezoid with four given side lengths?

What is the formula for finding the area of a trapezoid?

The formula for finding the area of a trapezoid is (1/2)(base1 + base2)(height), where base1 and base2 are the lengths of the parallel sides and height is the distance between the parallel sides.

Can I use the same formula for finding the area of any trapezoid?

Yes, the formula for finding the area of a trapezoid can be applied to any trapezoid, regardless of the lengths of the parallel sides or the height.

How do I know which side is the base and which side is the height in a trapezoid?

The base of a trapezoid is typically the longer of the two parallel sides, while the height is the distance between the two parallel sides.

Is there a specific unit for measuring the area of a trapezoid?

The area of a trapezoid can be measured in any unit of length, such as inches, centimeters, or meters. It is important to make sure that all measurements are in the same unit before plugging them into the formula.

Can the area of a trapezoid be negative?

No, the area of a trapezoid cannot be negative. It is a measurement of space, and therefore, will always be a positive value.

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