ABCD trapezoid

Since Ad and Bc are perpendicular....the length  of  one diagonal   is    12/sqrt (2)  + 4/sqrt (2)  =  16/sqrt (2)  = 8 sqrt (2)  = sqrt (128)

And the length of  portion of the base  from the red line to C =   8

So....the height of  the trapezoid is

h = sqrt [ ( sqrt (128))^2  - 8^2 ]  =  sqrt [ 128 - 64  ] =  sqrt [ 64]  = 8

So....the area of the trapezoid is

(1/2)  * height * ( sum of base lengths)  =

(1/2) (8)  ( 12 + 4)  =

4 (16)   =

64 units^2

ABCD trapezoid, bases AD = 4 and BC = 12.  Also, diagonals AC and BD are perpendicular.  Find the area of ABCD.

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ABCD trapezoid is an isosceles trapezoid with perpendicular diagonals.

Height      h = 1/2(AD + BC) = 8

Area       A = 1/2 [ h (AD + BC) ] = 64 u²