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The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid
have length 28, and the two diagonals of the trapezoid have length 52. What is the area of the
trapezoid?

 Jan 15, 2021
 #1
avatar+1028 
+3

The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid have a length of 28, and the two diagonals of the trapezoid have a length of 52. What is the area of the trapezoid?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Height      h = sqrt(282 - 152

 

Shorter Base      SB = sqrt(522 - h2) - 15

 

Longer Base      LB = SB + 30

 

Trapezoid area       A = 1/2 (SB + LB) * h

 Jan 15, 2021
 #3
avatar+1028 
+1

Trapezoid area    A = √1,199,055   laughlaughlaugh

jugoslav  Jan 16, 2021
edited by jugoslav  Jan 16, 2021
 #2
avatar+116126 
+1

Let  the shorter  base =  B

Let the longer base =  B + 30

 

1/2  the  difference in the bases  =  (B + 30  - B)  /2  =  15

 

We  can  find the height of the trapezoid as    sqrt ( 28^2 - 15^2)  = sqrt (559)

 

And we can find the length of the shorter base   as 

 

sqrt  [ 52^2 - (15+ B)^2]  = sqrt (559)

 

2704  - B^2  - 30B - 225   =  559

 

B^2  - 30B  -  1920  =  0

 

B = sqrt (2145 )  -  15

 

And the longer base =  sqrt (2145) + 15

 

Area = (1/2) sqrt (559)  (  2sqrt (2145) )   =     sqrt (559) sqrt (2145)   ≈  1095 units^2 

 

 

 

 

cool cool cool

 Jan 15, 2021

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