How do I find the area of a trapezoid?

The area of ​​an arbitrary trapezoid can be found using several formulas:
1.S = ((a + b) / 2) * h,
where S is the area of ​​the trapezoid, a and b are the smaller and larger base, respectively, h is the height.
2.S = m * h,
where m is the middle line of the trapezoid.
3.S = ((a + b) / (4 * (b – a)) * √ ((a + c + d – b) (a + d – b – c) (a + c – b – d) (b + c + d – a)),
where c and d are lateral sides.
4.S = ((a + b) / 2) * √ (c ^ 2 – 1/4 ((c ^ 2 – d ^ 2) / (b – a) + b – a) ^ 2).
The area of ​​an isosceles trapezoid can be found by the following formulas:
1.S = 4r ^ 2 / sinA,
where r is the radius of the circle inscribed in the trapezoid, A is the angle at the base of the trapezoid.
2.S = (b – c * cosƔ) c * sinƔ = (a + c * cos Ɣ) c * sinƔ,
where Ɣ is the angle between the large base b and the side.
3.S = ((a + b) / 2) * √ (c ^ 2 – 1/4 (b – a) ^ 2).



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