### Wong YX's answer to Silin's Primary 6 Maths Geometry Singapore question.

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For Q17(a):

To find area of one shaded part, we take area of big semicircle and minus area of small semicircle.

Diameter of big semicircle: 10 cm

Radius of big semicircle: 5 cm

Area: 3.14 x 5 x 5 ÷ 2 = 39.25 cm²

Diameter of small semicircle: 7 cm

Radius of big semicircle: 3.5 cm

Area: 3.14 x 3.5 x 3.5 ÷ 2 = 19.2325 cm²

Area of one shaded part:

39.25 - 19.2325 = 20.0175 cm²

Area of all shaded parts:

20.0175 x 2 = 40.035 cm² ≈ 40 cm²

For Q17(b):

Perimeter of one shaded part is the sum of:

(1) Arc length of big semicircle

(2) Arc length of small semicircle

(3) straight line at the bottom

Arc length of big semicircle is:

3.14 x 10 ÷ 2 = 15.7 cm

Arc length of small semicircle is:

3.14 x 7 ÷ 2 = 10.99 cm

Length of straight line:

10 - 7 = 3 cm

Perimeter of one shaded part:

15.7 + 10.99 + 3 = 29.69 cm

Perimeter of whole shaded part:

29.69 x 2 = 59.38 cm ≈ 59 cm

To find area of one shaded part, we take area of big semicircle and minus area of small semicircle.

Diameter of big semicircle: 10 cm

Radius of big semicircle: 5 cm

Area: 3.14 x 5 x 5 ÷ 2 = 39.25 cm²

Diameter of small semicircle: 7 cm

Radius of big semicircle: 3.5 cm

Area: 3.14 x 3.5 x 3.5 ÷ 2 = 19.2325 cm²

Area of one shaded part:

39.25 - 19.2325 = 20.0175 cm²

Area of all shaded parts:

20.0175 x 2 = 40.035 cm² ≈ 40 cm²

For Q17(b):

Perimeter of one shaded part is the sum of:

(1) Arc length of big semicircle

(2) Arc length of small semicircle

(3) straight line at the bottom

Arc length of big semicircle is:

3.14 x 10 ÷ 2 = 15.7 cm

Arc length of small semicircle is:

3.14 x 7 ÷ 2 = 10.99 cm

Length of straight line:

10 - 7 = 3 cm

Perimeter of one shaded part:

15.7 + 10.99 + 3 = 29.69 cm

Perimeter of whole shaded part:

29.69 x 2 = 59.38 cm ≈ 59 cm

Date Posted:
9 months ago