Trapezoid area with sides 11,16,24,27 equal to 274.077
where a and b are bases, h is height
where m is the middle line, h is the height
where d1,d2 are diagonals, α° is the angle between them
A trapezoid is a quadrilateral whose two sides are parallel (bases) and the other two are not parallel (sides).
Trapezoid area formula 
where a and b are the bases, c and d are the sides
where r is the radius of the inscribed circle, α° is the angle between the base and the sideSolution:
S =
a+b
2
·√c2 - ()2
(b-a)2+c2-d2
2·(b-a)
=
11+16
2
·√242 - ()2
(16-11)2+242-272
2·(16-11)
=
27
2
·√242 - ()2
52+242-272
2·5
=
27
2
·√576 - ()2
25+576-729
10
= 13.5
·√576 - ()2
-128
10
= 13.5
·√576 - (-12.8)2
= 13.5
·√576 - 163.84
= 13.5
·√412.16
= 13.5
·
20.302
=
274.077
Answer: trapezoid area with sides 11,16,24,27 equal to 274.077