What is the area of a receiving antennae with an angular spread of θ = λ/d?

[Biosyn]

Homework Statement

I just have a question on finding the area of a receiving antennae. The answer says the area is about 1km. I got an answer close to 1 km.

λ = 5*10^-2 m
d = 3*10³ m

The angular spread is θ = λ/d

θ= \frac{5*10^-2}{3*10³}

The spatial spread is the diameter of the beam on the target. So that means it is the angular spread times the distance the beam travels. Correct?

S = r*θ
S = (5*10^7 m ) * θ
S ≈ 1 km The area of the receiving antennae is them [1km / 2 ]² * ∏ = 0.78km which is about 1 km.

 

[haruspex]

The S ≈ 1 km approximation is rather rough. 830m is closer, and that leads to a final answer of about .54 km² (note: km², not km). This suggests you have an error somewhere else, but I'm not qualified to say where.