Further Mathematics Support Programme
Shaded circles 1 Answer
Area of small triangle
1
=2×𝑎×
=
2𝑎 − 𝑎 sin 60
4− 3 𝑎
=
2
𝑎
𝑎
𝑎2
Area of larger triangle
4− 3
1
=2×𝑎×
=
4− 3
4
2
𝑎
𝑎2
Area of kite
𝑎
𝑎
𝑎 sin 60
3
=
𝑎
2
Area of 6 kites = 6𝑎2
Area of small circle = 𝜋𝑎2
Shaded area = 6𝑎2 − 𝜋𝑎2 = 𝑎2 (6 − 𝜋)
Area of large circle = 4𝜋𝑎2
Shaded proportion =
3
4
3
2
6−𝜋
4𝜋
as a fraction. This is 22.7%
3
= 4 𝑎2 +
= 𝑎2
4− 3
4
𝑎2