A cardioid has a radius a of 4
Calculate the area and polar equations
Cardioid Area (A) formula
A = 6πa2
Plug in a = 4
A = 6π42
A = 6π(16)
A = 96π or 301.59289474462
Cardioid Arc Length (L) Formula
L = 16a
Plug in a = 4
L = 16(4)
L = 64
Polar equation of horizontal cardioid
r = a(1 ± cos(θ))
r = 4(1 ± cos(θ))
Polar equation of vertical cardioid
r = a(1 ± sin(θ))
r = 4(1 ± sin(θ))
Final Answers:
A = 96π or 301.59289474462
L = 64
r = 4(1 ± cos(θ))
r = 4(1 ± sin(θ))
L = 64
r = 4(1 ± cos(θ))
r = 4(1 ± sin(θ))
