GET TUTORING NEAR ME!

By providing your phone number, you consent to receive text messages from Club Z! for purposes related to our services. Message frequency may vary. Message and Data Rates may apply. Reply HELP for help or STOP to unsubscribe. See our Privacy Policy and our Terms and Conditions page

    Home / Get Math Help

    Convex Laminae

    Named laminae

    circular sector | circular segment | disk | 30-60-90 triangle | 3, 4, 5 triangle | diamond | filled ellipse | equilateral triangle | inverted equilateral triangle | golden rectangle | golden rhombus | golden triangle | half ellipse | half rectangle | half square | isosceles pentagon | isosceles right pentagon | isosceles right triangle | isosceles trapezoid | isosceles triangle | ... (total: 53)

    Definitions

    Defining inequalities

    x^2 + y^2<=a^2 and -tan(θ/2)<=x/y<=tan(θ/2) and y>=0

    x^2 + y^2<=a^2 and y>=a cos(θ/2)

    x^2 + y^2<=a^2

    y>=0 and sqrt(3) a>=2 (sqrt(3) x + y) and x>=0

    y>=0 and 12 a>=3 x + 4 y and x>=0

    abs(x)/a + abs(y)/b<=1

    x^2/a^2 + y^2/b^2<=1

    sqrt(3) (a + 3 x)>=3 y and sqrt(3) a + 6 y>=0 and sqrt(3) a>=3 (sqrt(3) x + y)

    sqrt(3) (a + 3 x)>=-3 y and sqrt(3) a>=6 y and sqrt(3) a + 3 y>=3 sqrt(3) x

    -a/2<=x<=a/2 and -(a ϕ)/2<=y<=(a ϕ)/2

    Lamina properties

    circular segment | (-sin(θ/2) a, cos(θ/2) a) | (sin(θ/2) a, cos(θ/2) a) 30-60-90 triangle | (0, 0) | (a/2, 0) | (0, (sqrt(3) a)/2) 3, 4, 5 triangle | (0, 3 a) | (0, 0) | (4 a, 0) diamond | (-a, 0) | (0, -b) | (a, 0) | (0, b) equilateral triangle | (0, a/sqrt(3)) | (-a/2, -a/(2 sqrt(3))) | (a/2, -a/(2 sqrt(3))) inverted equilateral triangle | (0, -a/sqrt(3)) | (a/2, a/(2 sqrt(3))) | (-a/2, a/(2 sqrt(3))) golden rectangle | (a/2, -(ϕ a)/2) | (a/2, (ϕ a)/2) | (-a/2, (ϕ a)/2) | (-a/2, -(ϕ a)/2) golden rhombus | (-a/(2 sqrt(5/8 - sqrt(5)/8)), 0) | (0, -a/(2 sqrt(5/8 + sqrt(5)/8))) | (a/(2 sqrt(5/8 - sqrt(5)/8)), 0) | (0, a/(2 sqrt(5/8 + sqrt(5)/8))) golden triangle | (-a/2, 0) | (a/2, 0) | (0, 1/2 sqrt(5 + 2 sqrt(5)) a) half rectangle | (-a/2, 0) | (a/2, 0) | (a/2, b/2) | (-a/2, b/2) half square | (-a/2, 0) | (a/2, 0) | (a/2, a/2) | (-a/2, a/2) isosceles pentagon | (-a/2, 0) | (a/2, 0) | (w, d) | (0, h) | (-w, d) isosceles right pentagon | (-a/2, 0) | (a/2, 0) | (a/2, b) | (0, h) | (-a/2, b) isosceles right triangle | (0, a) | (0, 0) | (a, 0) isosceles trapezoid | (-b/2, 0) | (b/2, 0) | (a/2, h) | (-a/2, h) isosceles triangle | (-a/2, 0) | (a/2, 0) | (0, h) Kepler triangle | (0, 0) | (sqrt(ϕ) a, 0) | (0, a) kite | (-sqrt(a^2 - h^2), 0) | (0, -h) | (sqrt(b^2 - h^2), 0) | (0, h) lozenge | (0, 0) | (a, 0) | ((1 + 1/sqrt(2)) a, a/sqrt(2)) | (a/sqrt(2), a/sqrt(2)) monokite | (0, 0) | ((sqrt(3) a)/2, (3 a)/2) | (0, 2 a) | (-(sqrt(3) a)/2, (3 a)/2) parallelogram | (0, 0) | (b, 0) | (cos(A) a + b, sin(A) a) | (cos(A) a, sin(A) a) pennant | (0, a/2) | (0, -a/2) | (h, 0) quarter rectangle | (0, 0) | (a/2, 0) | (a/2, b/2) | (0, b/2) quarter square | (0, 0) | (a/2, 0) | (a/2, a/2) | (0, a/2) rectangle | (-a/2, -b/2) | (a/2, -b/2) | (a/2, b/2) | (-a/2, b/2) regular decagon | (1/2 (1 + sqrt(5)) a, 0) | (1/4 (3 + sqrt(5)) a, sqrt(5/8 + sqrt(5)/8) a) | (a/2, 1/2 sqrt(5 + 2 sqrt(5)) a) | (-a/2, 1/2 sqrt(5 + 2 sqrt(5)) a) | (1/4 (-3 - sqrt(5)) a, sqrt(5/8 + sqrt(5)/8) a) | (1/2 (-1 - sqrt(5)) a, 0) | (1/4 (-3 - sqrt(5)) a, -1/2 sqrt(1/2 (5 + sqrt(5))) a) | (-a/2, -1/2 sqrt(5 + 2 sqrt(5)) a) | (a/2, -1/2 sqrt(5 + 2 sqrt(5)) a) | (1/4 (3 + sqrt(5)) a, -1/2 sqrt(1/2 (5 + sqrt(5))) a) regular diamond | (-a, 0) | (0, -a) | (a, 0) | (0, a) regular heptagon | (1/2 cos(π/14) csc(π/7) a, -1/2 csc(π/7) sin(π/14) a) | (1/2 cos((3 π)/14) csc(π/7) a, 1/2 csc(π/7) sin((3 π)/14) a) | (0, 1/2 csc(π/7) a) | (-1/2 cos((3 π)/14) csc(π/7) a, 1/2 csc(π/7) sin((3 π)/14) a) | (-1/2 cos(π/14) csc(π/7) a, -1/2 csc(π/7) sin(π/14) a) | (-a/2, -1/2 cot(π/7) a) | (a/2, -1/2 cot(π/7) a) regular hexagon | (a, 0) | (a/2, (sqrt(3) a)/2) | (-a/2, (sqrt(3) a)/2) | (-a, 0) | (-a/2, -(sqrt(3) a)/2) | (a/2, -(sqrt(3) a)/2) regular nonagon | (-1/2 cos(π/18) csc(π/9) a, 1/2 csc(π/9) sin(π/18) a) | (-1/4 sqrt(3) csc(π/9) a, -1/4 csc(π/9) a) | (-a/2, -1/2 cot(π/9) a) | (a/2, -1/2 cot(π/9) a) | (1/4 sqrt(3) csc(π/9) a, -1/4 csc(π/9) a) | (1/2 cos(π/18) csc(π/9) a, 1/2 csc(π/9) sin(π/18) a) | (1/2 csc(π/9) sin((2 π)/9) a, 1/2 cos((2 π)/9) csc(π/9) a) | (0, 1/2 csc(π/9) a) | (-1/2 csc(π/9) sin((2 π)/9) a, 1/2 cos((2 π)/9) csc(π/9) a) regular octagon | (1/2 cot(π/8) a, a/2) | (a/2, 1/2 cot(π/8) a) | (-a/2, 1/2 cot(π/8) a) | (-1/2 cot(π/8) a, a/2) | (-1/2 cot(π/8) a, -a/2) | (-a/2, -1/2 cot(π/8) a) | (a/2, -1/2 cot(π/8) a) | (1/2 cot(π/8) a, -a/2) regular pentagon | (1/4 (1 + sqrt(5)) a, root of 1 - 20 x^2 + 80 x^4 near x = 0.262866 a) | (0, sqrt(1/10 (5 + sqrt(5))) a) | (1/4 (-1 - sqrt(5)) a, root of 1 - 20 x^2 + 80 x^4 near x = 0.262866 a) | (-a/2, -1/2 sqrt(1 + 2/sqrt(5)) a) | (a/2, -1/2 sqrt(1 + 2/sqrt(5)) a) rhombus | (-cos(θ) a, 0) | (0, -sin(θ) a) | (cos(θ) a, 0) | (0, sin(θ) a) right trapezoid | (0, 0) | (a, 0) | (a, h_2) | (0, h_1) right triangle | (0, 0) | (a, 0) | (0, b) scalene triangle | (c, 0) | ((-a^2 + b^2 + c^2)/(2 c), sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))/(2 c)) | (0, 0) square | (-a/2, -a/2) | (a/2, -a/2) | (a/2, a/2) | (-a/2, a/2) 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))) triangle | (c, 0) | ((-a^2 + b^2 + c^2)/(2 c), sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))/(2 c)) | (0, 0) inverted isosceles trapezoid | (-b/2, 0) | (b/2, 0) | (a/2, sqrt(-1/4 (-a + b)^2 + c^2)) | (-a/2, sqrt(-1/4 (-a + b)^2 + c^2))

    circular segment | 2 30-60-90 triangle | 3 3, 4, 5 triangle | 3 diamond | 4 equilateral triangle | 3 inverted equilateral triangle | 3 golden rectangle | 4 golden rhombus | 4 golden triangle | 3 half rectangle | 4 half square | 4 isosceles pentagon | 5 isosceles right pentagon | 5 isosceles right triangle | 3 isosceles trapezoid | 4 isosceles triangle | 3 Kepler triangle | 3 kite | 4 lozenge | 4 monokite | 4 parallelogram | 4 pennant | 3 quarter rectangle | 4 quarter square | 4 rectangle | 4 regular decagon | 10 regular diamond | 4 regular heptagon | 7 regular hexagon | 6 regular nonagon | 9 regular octagon | 8 regular pentagon | 5 rhombus | 4 right trapezoid | 4 right triangle | 3 scalene triangle | 3 square | 4 trapezoid | 4 triangle | 3 inverted isosceles trapezoid | 4

    circular sector | a>0 and 0<θ<π circular segment | a>0 and 0<θ<π disk | a>0 30-60-90 triangle | a>0 3, 4, 5 triangle | a>0 diamond | a>0 and b>0 filled ellipse | a>0 and b>0 equilateral triangle | a>0 inverted equilateral triangle | a>0 golden rectangle | a>0 golden rhombus | a>0 golden triangle | a>0 half ellipse | a>0 and b>0 half rectangle | a>0 and b>0 half square | a>0 isosceles pentagon | 00 and 00 isosceles trapezoid | 00 isosceles triangle | a>0 and h>0 Kepler triangle | a>0 kite | 00 monokite | a>0 parallelogram | a>0 and b>0 and 00 and h>0 quarter ellipse | a>0 and b>0 quarter rectangle | a>0 and b>0 quarter square | a>0 rectangle | a>0 and b>0 regular decagon | a>0 regular diamond | a>0 regular heptagon | a>0 regular hexagon | a>0 regular nonagon | a>0 regular octagon | a>0 regular pentagon | a>0 rhombus | a>0 and 0<θ<π/2 right trapezoid | a>0 and h_1>0 and h_2>0 right triangle | a>0 and b>0 scalene triangle | a>0 and b>0 and c>0 and a + b>c and b + c>a and a + c>b and a!=b!=c square | a>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 triangle | a>0 and b>0 and c>0 and a + b>c and b + c>a and a + c>b half-disk | a>0 inverted isosceles trapezoid | 0(a - b)/2 asymmetric lens | R>0 and r>0 and abs(R - r)0 Reuleaux triangle | a>0 rounded rectangle | a>0 and b>0 and r>0 stadium | a>0 and r>0 vesica piscis | a>0

    diamond | 2 a | 2 b golden rectangle | a sqrt(ϕ^2 + 1) | a sqrt(ϕ^2 + 1) golden rhombus | a/sqrt(5/8 - sqrt(5)/8) | a/sqrt(5/8 + sqrt(5)/8) isosceles pentagon | sqrt(1/4 (a + 2 w)^2 + d^2) | sqrt(a^2/4 + h^2) | sqrt(a^2/4 + h^2) | sqrt((a/2 + w)^2 + d^2) | 2 w isosceles right pentagon | sqrt(a^2 + b^2) | sqrt(a^2/4 + h^2) | sqrt(a^2/4 + h^2) | sqrt(a^2 + b^2) | a isosceles trapezoid | 1/2 sqrt((a + b)^2 + 4 h^2) | 1/2 sqrt((a + b)^2 + 4 h^2) kite | sqrt(a^2 - h^2) + sqrt(b^2 - h^2) | 2 h lozenge | sqrt(2 + sqrt(2)) a | sqrt(2 - sqrt(2)) a monokite | 2 a | sqrt(3) a parallelogram | sqrt(a^2 - 2 a b cos(A) + b^2) | sqrt(a^2 + 2 a b cos(A) + b^2) rectangle | sqrt(a^2 + b^2) | sqrt(a^2 + b^2) regular decagon | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | sqrt(1/2 (5 + sqrt(5))) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | 1/2 (3 + sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | sqrt(5 + 2 sqrt(5)) a | (1 + sqrt(5)) a | (1 + sqrt(5)) a | (1 + sqrt(5)) a | (1 + sqrt(5)) a | (1 + sqrt(5)) a regular diamond | 2 a | 2 a regular heptagon | a root of x^3 - x^2 - 2 x + 1 near x = 1.80194 | a root of x^3 - x^2 - 2 x + 1 near x = 1.80194 | a root of x^3 - x^2 - 2 x + 1 near x = 1.80194 | a root of x^3 - x^2 - 2 x + 1 near x = 1.80194 | a root of x^3 - x^2 - 2 x + 1 near x = 1.80194 | a root of x^3 - x^2 - 2 x + 1 near x = 1.80194 | a root of x^3 - x^2 - 2 x + 1 near x = 1.80194 | a root of x^3 - 2 x^2 - x + 1 near x = 2.24698 | a root of x^3 - 2 x^2 - x + 1 near x = 2.24698 | a root of x^3 - 2 x^2 - x + 1 near x = 2.24698 | a root of x^3 - 2 x^2 - x + 1 near x = 2.24698 | a root of x^3 - 2 x^2 - x + 1 near x = 2.24698 | a root of x^3 - 2 x^2 - x + 1 near x = 2.24698 | a root of x^3 - 2 x^2 - x + 1 near x = 2.24698 regular hexagon | sqrt(3) a | sqrt(3) a | sqrt(3) a | sqrt(3) a | sqrt(3) a | sqrt(3) a | 2 a | 2 a | 2 a regular nonagon | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x - 1 near x = 1.87939 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 3 near x = 2.53209 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 | a root of x^3 - 3 x^2 + 1 near x = 2.87939 regular octagon | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | sqrt(2 (2 + sqrt(2))) a | sqrt(2 (2 + sqrt(2))) a | sqrt(2 (2 + sqrt(2))) a | sqrt(2 (2 + sqrt(2))) a regular pentagon | a ϕ | a ϕ | a ϕ | a ϕ | a ϕ rhombus | 2 a cos(θ) | 2 a sin(θ) right trapezoid | sqrt(a^2 + h_1^2) | sqrt(a^2 + h_2^2) square | sqrt(2) a | sqrt(2) a 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)) inverted isosceles trapezoid | sqrt(a b + c^2) | sqrt(a b + c^2)

    circular sector | r = a cos(θ/2) circular segment | r = a cos(θ/2) equilateral triangle | r = a/(2 sqrt(3)) inverted equilateral triangle | r = a/(2 sqrt(3)) regular decagon | r = 1/2 sqrt(5 + 2 sqrt(5)) a regular heptagon | r = 1/2 a cot(π/7) regular hexagon | r = (sqrt(3) a)/2 regular nonagon | r = 1/2 a cot(π/9) regular octagon | r = 1/2 (1 + sqrt(2)) a regular pentagon | r = 1/10 sqrt(25 + 10 sqrt(5)) a square | r = a/2

    circular sector | h = a (1 - cos(θ/2)) circular segment | h = a (1 - cos(θ/2)) equilateral triangle | h = a/(2 sqrt(3)) inverted equilateral triangle | h = a/(2 sqrt(3)) regular decagon | h = 1/2 (1 + sqrt(5) - sqrt(5 + 2 sqrt(5))) a regular heptagon | h = 1/2 a tan(π/14) regular hexagon | h = -1/2 (sqrt(3) - 2) a regular nonagon | h = 1/2 a tan(π/18) regular octagon | h = 1/2 (-1 - sqrt(2) + sqrt(2 (2 + sqrt(2)))) a regular pentagon | h = 1/2 sqrt(1 - 2/sqrt(5)) a square | h = 1/2 (sqrt(2) - 1) a

    circular sector | a (1 - cos(θ/2)) circular segment | a cos(θ/2) 30-60-90 triangle | (sqrt(3) a)/2 3, 4, 5 triangle | 3 a equilateral triangle | (sqrt(3) a)/2 inverted equilateral triangle | (sqrt(3) a)/2 golden rectangle | a ϕ golden triangle | 1/2 sqrt(5 + 2 sqrt(5)) a half rectangle | b/2 half square | a/2 isosceles pentagon | h isosceles right pentagon | h isosceles right triangle | a isosceles trapezoid | h isosceles triangle | h Kepler triangle | a monokite | 2 a parallelogram | a sin(A) pennant | a quarter rectangle | b/2 quarter square | a/2 rectangle | b regular pentagon | 1/2 sqrt(5 + 2 sqrt(5)) a right triangle | b scalene triangle | sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))/(2 c) square | a trapezoid | sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (b - a)) triangle | sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))/(2 c) inverted isosceles trapezoid | sqrt(c^2 - 1/4 (b - a)^2)

    circular sector | A = (a^2 θ)/2 circular segment | A = 1/2 a^2 (θ - sin(θ)) disk | A = π a^2 30-60-90 triangle | A = (sqrt(3) a^2)/8 3, 4, 5 triangle | A = 6 a^2 diamond | A = 2 a b filled ellipse | A = π a b equilateral triangle | A = (sqrt(3) a^2)/4 inverted equilateral triangle | A = (sqrt(3) a^2)/4 golden rectangle | A = a^2 ϕ golden rhombus | A = (2 a^2)/sqrt(5) golden triangle | A = 1/4 sqrt(5 + 2 sqrt(5)) a^2 half ellipse | A = (π a b)/2 half rectangle | A = (a b)/2 half square | A = a^2/2 isosceles pentagon | A = (a d)/2 + h w isosceles right pentagon | A = 1/2 a (b + h) isosceles right triangle | A = a^2/2 isosceles trapezoid | A = 1/2 h (a + b) isosceles triangle | A = (a h)/2 Kepler triangle | A = (a^2 sqrt(ϕ))/2 kite | A = h (sqrt(a^2 - h^2) + sqrt(b^2 - h^2)) lozenge | A = a^2/sqrt(2) monokite | A = sqrt(3) a^2 parallelogram | A = a b sin(A) pennant | A = (a h)/2 quarter ellipse | A = (π a b)/4 quarter rectangle | A = (a b)/4 quarter square | A = a^2/4 rectangle | A = a b regular decagon | A = 5/2 sqrt(5 + 2 sqrt(5)) a^2 regular diamond | A = 2 a^2 regular heptagon | A = 7/4 a^2 cot(π/7) regular hexagon | A = (3 sqrt(3) a^2)/2 regular nonagon | A = 9/4 a^2 cot(π/9) regular octagon | A = 2 (1 + sqrt(2)) a^2 regular pentagon | A = 5/4 sqrt(1 + 2/sqrt(5)) a^2 rhombus | A = a^2 sin(2 θ) right trapezoid | A = 1/2 a (h_1 + h_2) right triangle | A = (a b)/2 scalene triangle | A = 1/4 sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c)) square | A = a^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)) triangle | A = 1/4 sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c)) half-disk | A = (π a^2)/2 inverted isosceles trapezoid | A = 1/4 (a + b) sqrt(4 c^2 - (b - a)^2) asymmetric lens | A = r^2 cos^(-1)((d^2 + r^2 - R^2)/(2 d r)) + R^2 cos^(-1)((d^2 - r^2 + R^2)/(2 d R)) - 1/2 sqrt((d + r - R) (d - r + R) (-d + r + R) (d + r + R)) symmetric lens | A = -1/2 d sqrt(4 a^2 - d^2) - 2 a^2 tan^(-1)(d/sqrt(4 a^2 - d^2)) + π a^2 quarter disk | A = (π a^2)/4 Reuleaux triangle | A = 1/2 (π - sqrt(3)) a^2 rounded rectangle | A = 2 r (a + b) + a b + π r^2 stadium | A = 2 a r + π r^2 vesica piscis | A = 1/6 (4 π - 3 sqrt(3)) a^2

    circular sector | x^_ = (0, 2/3 sinc(θ/2) a) circular segment | x^_ = (0, (4 sin^3(θ/2) a)/(3 (-sin(θ) + θ))) disk | x^_ = (0, 0) 30-60-90 triangle | x^_ = (a/6, a/(2 sqrt(3))) 3, 4, 5 triangle | x^_ = ((4 a)/3, a) diamond | x^_ = (0, 0) filled ellipse | x^_ = (0, 0) equilateral triangle | x^_ = (0, 0) inverted equilateral triangle | x^_ = (0, 0) golden rectangle | x^_ = (0, 0) golden rhombus | x^_ = (0, 0) golden triangle | x^_ = (0, 1/6 sqrt(5 + 2 sqrt(5)) a) half ellipse | x^_ = (0, (4 b)/(3 π)) half rectangle | x^_ = (0, b/4) half square | x^_ = (0, a/4) isosceles pentagon | x^_ = (0, (a d^2 + 2 h (d + h) w)/(3 a d + 6 h w)) isosceles right pentagon | x^_ = (0, 1/3 (h + b^2/(b + h))) isosceles right triangle | x^_ = (a/3, a/3) isosceles trapezoid | x^_ = (0, ((2 a + b) h)/(3 (a + b))) isosceles triangle | x^_ = (0, h/3) Kepler triangle | x^_ = ((sqrt(ϕ) a)/3, a/3) kite | x^_ = (1/3 (-sqrt(a^2 - h^2) + sqrt(b^2 - h^2)), 0) lozenge | x^_ = (1/4 (2 + sqrt(2)) a, a/(2 sqrt(2))) monokite | x^_ = (0, (7 a)/6) parallelogram | x^_ = (1/2 (cos(A) a + b), 1/2 sin(A) a) pennant | x^_ = (h/3, 0) quarter ellipse | x^_ = ((4 a)/(3 π), (4 b)/(3 π)) quarter rectangle | x^_ = (a/4, b/4) quarter square | x^_ = (a/4, a/4) rectangle | x^_ = (0, 0) regular decagon | x^_ = (0, 0) regular diamond | x^_ = (0, 0) regular heptagon | x^_ = (0, 0) regular hexagon | x^_ = (0, 0) regular nonagon | x^_ = (0, 0) regular octagon | x^_ = (0, 0) regular pentagon | x^_ = (0, 0) rhombus | x^_ = (0, 0) 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))) right triangle | x^_ = (a/3, b/3) scalene triangle | x^_ = ((-a^2 + b^2 + 3 c^2)/(6 c), sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))/(6 c)) square | x^_ = (0, 0) 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))) triangle | x^_ = ((-a^2 + b^2 + 3 c^2)/(6 c), sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))/(6 c)) half-disk | x^_ = (0, (4 a)/(3 π)) inverted isosceles trapezoid | x^_ = (0, ((2 a + b) sqrt(-(-a + b)^2 + 4 c^2))/(6 (a + b))) symmetric lens | x^_ = (0, 0) quarter disk | x^_ = ((4 a)/(3 π), (4 a)/(3 π)) Reuleaux triangle | x^_ = (0, 0) rounded rectangle | x^_ = (0, 0) stadium | x^_ = (0, 0) vesica piscis | x^_ = (0, 0)