In the pictures below, find the difference between the areas of the ci

1.	In the pictures below, find the difference between the areas of the circle and the polygon, up to two decimal places.
Answer» i. Radius of the small circle = 2 cm Area = π × 2² = 3.14 × 4 = 12.56 cm² Daigonal of the square = 4 cm One side of the square = 4/√2 cm Area of the square = \(\frac{4}{\sqrt{2}}\times\frac{4}{\sqrt{2}}=\frac{16}{2}=8 \,cm\) Differences between the areas = 12.56 – 8 = 4.56 cm ii. Radius of the circle = 2 cm Area= π × 2² = 3.14 × 4 = 12.56 cm² One side of the regular hexagon = 2 cm Area of the regular hexagon = \(6\times\frac{\sqrt{3}\times2^2}{4}=6\sqrt{3}\) = 6 × 1.73 = 10.38 cm² Differences between the areas = 12.56 – 10.38 = 2.18 cm²

In the pictures below, find the difference between the areas of the circle and the polygon, up to two decimal places.

Answer»

i. Radius of the small circle = 2 cm

Area = π × 2² = 3.14 × 4

= 12.56 cm²

Daigonal of the square = 4 cm

One side of the square = 4/√2 cm

Area of the square = \(\frac{4}{\sqrt{2}}\times\frac{4}{\sqrt{2}}=\frac{16}{2}=8 \,cm\)

Differences between the areas = 12.56 – 8 = 4.56 cm

ii. Radius of the circle = 2 cm

Area= π × 2² = 3.14 × 4 = 12.56 cm²

One side of the regular hexagon = 2 cm

Area of the regular hexagon = \(6\times\frac{\sqrt{3}\times2^2}{4}=6\sqrt{3}\)

= 6 × 1.73 = 10.38 cm²

Differences between the areas = 12.56 – 10.38 = 2.18 cm²

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