right trapezoid | trapezoid
y>=0 and a>=x and a h_1 + h_2 x>=a y + h_1 x and x>=0
y>=0 and y (a^2 - c^2 + d^2) + x sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + b^2 y<=b (sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + 2 a y) and sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + 2 a y>=2 b y and x sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) + 2 a b y>=y (a^2 + b^2 + c^2 - d^2)
right trapezoid | (0, 0) | (a, 0) | (a, h_2) | (0, h_1) trapezoid | (0, 0) | (b, 0) | ((a^2 - b^2 - c^2 + d^2)/(2 (a - b)), sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (-a + b))) | (-(a^2 - 2 a b + b^2 + c^2 - d^2)/(2 (a - b)), sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (-a + b)))
right trapezoid | 4 trapezoid | 4
right trapezoid | a>0 and h_1>0 and h_2>0 trapezoid | a>0 and b>0 and c>0 and d>0 and (a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)>0
right trapezoid | sqrt(a^2 + h_1^2) | sqrt(a^2 + h_2^2) trapezoid | sqrt((a^2 (-b) + a b^2 - a c^2 + b d^2)/(b - a)) | sqrt((a^2 (-b) + a b^2 - a d^2 + b c^2)/(b - a))
trapezoid | sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (b - a))
right trapezoid | A = 1/2 a (h_1 + h_2) trapezoid | A = ((a + b) sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(4 (b - a))
right trapezoid | x^_ = ((a (h_1 + 2 h_2))/(3 (h_1 + h_2)), 1/3 (h_2 + h_1^2/(h_1 + h_2))) trapezoid | x^_ = (b/2 + ((2 a + b) (c^2 - d^2))/(6 (-a^2 + b^2)), ((2 a + b) sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(6 (-a^2 + b^2)))
right trapezoid | J_x invisible comma x = 1/12 a (h_1 + h_2) (h_1^2 + h_2^2) trapezoid | J_x invisible comma x = -((3 a + b) ((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))^(3/2))/(96 (a - b)^3)
right trapezoid | J_y invisible comma y = 1/12 a^3 (h_1 + 3 h_2) trapezoid | J_y invisible comma y = -(sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) (a^5 - a^4 b + 6 a^3 b^2 - 6 a^2 b^3 - 8 a^2 b c^2 + 8 a^2 b d^2 - 7 a b^4 + 4 a b^2 c^2 - 4 a b^2 d^2 + 3 a c^4 - 6 a c^2 d^2 + 3 a d^4 + 7 b^5 + 4 b^3 c^2 - 4 b^3 d^2 + b c^4 - 2 b c^2 d^2 + b d^4))/(96 (a - b)^3)
right trapezoid | J_zz = 1/12 a (a^2 (h_1 + 3 h_2) + (h_1 + h_2) (h_1^2 + h_2^2)) trapezoid | J_zz = (sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) (a^4 - 4 a^3 b - 3 a^2 (c^2 + d^2) + a b (6 c^2 - 2 d^2) + b^2 (3 b^2 + 3 c^2 - d^2)))/(48 (a - b)^2)
right trapezoid | J_x invisible comma y = -1/24 a^2 (h_1^2 + 2 h_2 h_1 + 3 h_2^2) trapezoid | J_x invisible comma y = ((a - b - c - d) (a - b + c - d) (a - b - c + d) (a - b + c + d) (2 b (2 a^2 + c^2) - (a + b) (2 b^2 + 3 c^2) + d^2 (3 a + b)))/(96 (a - b)^3)
right trapezoid | r_x = sqrt(h_1^2 + h_2^2)/sqrt(6) r_y = (a sqrt((h_1 + 3 h_2)/(h_1 + h_2)))/sqrt(6)
right trapezoid | a | h_2 | sqrt(a^2 + (h_2 - h_1)^2) | h_1 trapezoid | b | d | a | c
right trapezoid | p = sqrt(a^2 + (h_2 - h_1)^2) + a + h_1 + h_2 trapezoid | p = a + b + c + d
right trapezoid | max(sqrt(a^2 + h_1^2), sqrt(a^2 + h_2^2)) trapezoid | max(b, sqrt((a^2 b - a b^2 + a d^2 - b c^2)/(a - b)), sqrt((a^2 b - a b^2 + a c^2 - b d^2)/(a - b)))
right trapezoid | χ = 1 trapezoid | χ = 1
convex laminae | polygonal laminae | quadrilateral laminae | scalene quadrilateral laminae
