CONCEPT OF SIMILAR FIGURES

Question AThe figure is made up of a big semi circle and 2 small semi circles with diameter of 14 cm and 28 cm respectively. Find the perimeter and area of the shaded part. Use calculator . (Round off your answer to the nearest whole number)

Perimeter of shaded part• Big semi circle + small circle

Solution - Perimeter

• × d × ½ + × d• × 28 × ½ + × 14• 14 + 14 = 28 ≈ 88 cm

Perimeter of shaded part• Big semi circle + small circle

Solution - Perimeter

• 14 + 14 = 28 ≈ 88 cm

Do you notice that the perimeter of the big semi circle and the 2 small semi circle is the same? Therefore we can use the perimeter of 1 big circle to find the answer.

Alternative method

• × d = × 28 ≈ 88 cm

Conclusion

As long as the different semi circles (or circles) are joined together to form an enclosed shape, the sum of all the small semi circles (or circles) will be equal to the perimeter of the big semi circles (big circles).

Area of shaded part• Big semi circle ‒ small circle

Solution – Area of shaded part

• × r2 × ½ ‒ × r2

• × 14 × 14 × ½ ‒ × 7 × 7• 98 ‒ 49 = 49 ≈ 154 cm2

Area of shaded part• Radius of big semi circle – 14 cm• Radius of small semi circle – 7 cm

Solution – Area of shaded part

Ratio of Radius (S) : Radius (B) = 7 : 14 = 1 : 2Area of shaded part

• Area of big semi circle – × 14 cm × 14 cm × ½ = (98)cm2 • Radius of small semi circle– × 7 cm × 7 cm × ½ = (24.5) cm2

Area (Small) : Area (Big) = 24.5 : 98 = 1 : 4

Area of shaded part• Radius of small semi-circle : Radius of big semi-circle 7 : 14 = 1 : 2

Alternative solution – Area of shaded part

Area of small semi-circle : Area of big semi-circle 1 × 1 : 2 × 2 = 1 : 4

2 units

1 unit 1 unit

Shaded area 4u ‒ 1u ‒ 1u = 2u

Area of 1 small semi-circle × 7 × 7 × ½ ≈ 77 cm2

Shaded area 77 × 2 = 154 cm2

Question BThe figure is made up of a big semi circle and 3 small semi circles with radii of 30 cm and 10 cm respectively. Find the perimeter and area of the shaded part. Use calculator . (Round off your answer to the nearest whole number)

Perimeter of shaded part• Since the 3 small semi-circles are joined to the

big semi-circle to form an enclosed shape, the perimeter of the 3 semi-circles will equal to the perimeter of the big semi-circle.

Solution - Perimeter

• × d

• × 60 = (60) cm ≈ 188 cm

Radius (Small) : Radius (Big) 10 : 30 = 1 : 3

Solution – Area of shaded part

Area (Small) : Area (Big) 1 × 1 : 3 × 3 = 1 : 9

1 unit 1 unit 1 unit

6 units

Area of 1 small semi-circle (1u) × ½ × 10 × 10 = (50)cm2

Area of shaded part 9u ‒ 1u ‒ 1u ‒ 1u = 6u

Area of shaded part 50 × 6u ≈ 942 cm2