http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

Kungfu Math

Name:________________________ Class:_______ Date:________

Scroll: Ratio >> Repeated Identity >> ps (3466)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

1) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 1:4.Area D is 25 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the area of the circle.

Answer:_______________ cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

2) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 5:4 and the ratio of Area B to Area C is 4:3.Area D is 12 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the length of one side of the square.

Answer:_______________ cm

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

3) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 5:11 and the ratio of Area B to Area C is 11:4.Area D is 24 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the length of one side of the square.

Answer:_______________ cm

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

4) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 3:7.Area D is 30 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the area of the circle.

Answer:_______________ cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

5) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 1:4.Area D is 40 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the total area of A, B and C.

Answer:_______________ cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

6) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 13:12 and the ratio of Area B to Area C is 12:13.Area D is 24 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the length of one side of the square.

Answer:_______________ cm

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

7) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 5:1 and the ratio of Area B to Area C is 1:4.Area D is 6 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the length of one side of the square.

Answer:_______________ cm

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

8) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 2:3.Area D is 15 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the area of C.

Answer:_______________ cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

9) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 11:7 and the ratio of Area B to Area C is 14:16.Area D is 10 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the length of one side of the square.

Answer:_______________ cm

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

10) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 2:3.Area D is 30 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer:_______________

b) Find the area of the circle.

Answer:_______________ cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

1) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 1:4.Area D is 25 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:2:8 or 5 : 2 : 8

b) Find the area of the circle.

Answer : 100 cm2

SOLUTION 1 :

a)

A + D = B + C

A : D B : C1 x 5 : 1 x 5 1 x 2 : 4 x 2

5 : 5 2 : 8

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

A : B : C5 : 2 : 8

The ratio is 5:2:8.

b)

Step 1: A + D → 5 units + 5 units = 10 unitsStep 2: D → 5 units 5 units → 25 cm 2

1 unit → 25 ÷ 5 = 5 cm 2

Step 3: A + B + C + D → 5 units + 2 units + 8 units + 5 units = 20 units 20 units = 20 x 5 cm 2

= 100 cm²

The area of the circle is 100 cm 2.

2) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 5:4 and the ratio of Area B to Area C is 4:3.Area D is 12 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:4:3 or 5 : 4 : 3

b) Find the length of one side of the square.

Answer : 6 cm

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

SOLUTION 1 :

a)

A : B5 : 4

B : C4 : 3

A : B : C5 : 4 : 3

The ratio is 5:4:3.

b)

Step 1: A + B → 5 units + 4 units = 9 unitsStep 2: C + D → 9 units A + B + C + D → 2 x 9 units = 18 units D → 9 units - 3 units = 6 unitsStep 3: 6 units = 12 cm² 1 unit = 12 ÷ 6 = 2 cm² 18 units = 18 x 2 = 36 cm²

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

Step 4: 6 x 6 = 36 cm²

The length of one side of the square is 6 cm.

3) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 5:11 and the ratio of Area B to Area C is 11:4.Area D is 24 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:11:4 or 5 : 11 : 4

b) Find the length of one side of the square.

Answer : 8 cm

SOLUTION 1 :

a)

A : B5 : 11

B : C11 : 4

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

A : B : C5 : 11 : 4

The ratio is 5:11:4.

b)

Step 1: A + B → 5 units + 11 units = 16 unitsStep 2: C + D → 16 units A + B + C + D → 2 x 16 units = 32 units D → 16 units - 4 units = 12 unitsStep 3: 12 units = 24 cm² 1 unit = 24 ÷ 12 = 2 cm² 32 units = 32 x 2 = 64 cm²Step 4: 8 x 8 = 64 cm²

The length of one side of the square is 8 cm.

4) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 3:7.Area D is 30 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:3:7 or 5 : 3 : 7

b) Find the area of the circle.

Answer : 120 cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

SOLUTION 1 :

a)

A + D = B + C

A : D B : C1 x 5 : 1 x 5 3 : 7

5 : 5

A : B : C5 : 3 : 7

The ratio is 5:3:7.

b)

Step 1: A + D → 5 units + 5 units = 10 unitsStep 2: D → 5 units 5 units → 30 cm 2

1 unit → 30 ÷ 5 = 6 cm 2

Step 3: A + B + C + D → 5 units + 3 units + 7 units + 5 units

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

= 20 units 20 units = 20 x 6 cm 2

= 120 cm²

The area of the circle is 120 cm 2.

5) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 1:4.Area D is 40 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:2:8 or 5 : 2 : 8

b) Find the total area of A, B and C.

Answer : 120 cm2

SOLUTION 1 :

a)

A + D = B + C

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

A : D B : C1 x 5 : 1 x 5 1 x 2 : 4 x 2

5 : 5 2 : 8

A : B : C5 : 2 : 8

The ratio is 5:2:8.

b)

Step 1: A + D → 5 units + 5 units = 10 unitsStep 2: D → 5 units 5 units → 40 cm 2

1 unit → 40 ÷ 5 = 8 cm 2

Step 3: A + B + C → 5 units + 2 units + 8 units = 15 units 15 units = 15 x 8 cm 2

= 120 cm²

The toal area of A, B and C is 120 cm 2.

6) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 13:12 and the ratio of Area B to Area C is 12:13.Area D is 24 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 13:12:13 or 13 : 12 : 13

b) Find the length of one side of the square.

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

Answer : 10 cm

SOLUTION 1 :

a)

A : B13 : 12

B : C12 : 13

A : B : C13 : 12 : 13

The ratio is 13:12:13.

b)

Step 1: A + B → 13 units + 12 unit = 25 unitsStep 2: C + D → 25 units A + B + C + D → 2 x 25 units = 50 units D → 25units - 13 units = 12 unitsStep 3: 12 units = 24 cm² 1 unit = 24 cm 2 ÷ 12 units = 2 cm² 50 units = 50 x 2 cm 2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

= 100 cm²Step 4: 10 x 10 = 100 cm²

The length of one side of the square is 10 cm.

7) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 5:1 and the ratio of Area B to Area C is 1:4.Area D is 6 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:1:4 or 5 : 1 : 4

b) Find the length of one side of the square.

Answer : 6 cm

SOLUTION 1 :

a)

A : B5 : 1

B : C1 : 4

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

A : B : C5 : 1 : 4

The ratio is 5:1:4.

b)

Step 1: A + B → 5 units + 1 units = 6 unitsStep 2: C + D → 6 units A + B + C + D → 2 x 6 units = 12 units D → 6 units - 4 units = 2 unitsStep 3: 2 units = 6 cm² 1 unit = 6 ÷ 2 = 3 cm² 12 units = 12 x 3 = 36 cm²Step 4: 6 x 6 = 36 cm²

The length of one side of the square is 6 cm.

8) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 2:3.Area D is 15 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:4:6 or 5 : 4 : 6

b) Find the area of C.

Answer : 18 cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

SOLUTION 1 :

a)

A + D = B + C

A : D B : C1 x 5 : 1 x 5 2 x 2 : 3 x 2

5 : 5 4 : 6

A : B : C5 : 4 : 6

The ratio is 5:4:6.

b)

Step 1: A + D → 5 units + 5 units = 10 unitsStep 2: D → 5 units 5 units → 15 cm 2

1 unit → 15 ÷ 5 = 3 cm 2

Step 3: 6 units = 6 x 3 cm 2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

= 18 cm²

The area of C is 18 cm 2.

9) The figure below is not drawn to scale. It shows a square which is divided into 4 parts, A, B, C and D. The line RS divides the square into 2 equal parts. The ratio of Area A to Area B is 11:7 and the ratio of Area B to Area C is 14:16.Area D is 10 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 11:7:8 or 11 : 7 : 8

b) Find the length of one side of the square.

Answer : 6 cm

SOLUTION 1 :

a)

A : B11 : 7

B : C14 ÷ 2 :

16 ÷ 2

7 : 8

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

A : B : C11 : 7 : 8

The ratio is 11:7:8.

(b)

Step 1: A + B → 11 units + 7 unit = 18 unitsStep 2: C + D → 18 units A + B + C + D → 2 x 18 units = 36 units D → 18 units - 8 units = 10 unitsStep 3: 10 units = 10 cm² 1 unit = 10 cm 2 ÷ 10 units = 1 cm² 36 units = 36 x 1 cm 2

= 36 cm²Step 4: 6 x 6 = 36 cm²

The length of one side of the square is 6 cm.

10) The figure below is not drawn to scale. It shows a circle which is divided into 4 parts, A, B, C and D. The line RS divides the circle into 2 equal parts. The ratio of Area A to Area D is 1:1 and the ratio of Area B to Area C is 2:3.Area D is 30 cm².

a) Find the ratio of Area A to Area B to Area C.

Answer : 5:4:6 or 5 : 4 : 6

b) Find the area of the circle.

Answer : 120 cm2

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

SOLUTION 1 :

a)

A + D = B + C

A : D B : C1 x 5 : 1 x 5 2 x 2 : 3 x 2

5 : 5 4 : 6

A : B : C5 : 4 : 6

The ratio is 5:4:6.

b)

Step 1: A + D → 5 units + 5 units = 10 unitsStep 2: D → 5 units 5 units → 30 cm 2

1 unit → 30 ÷ 5 = 6 cm 2

Step 3: A + B + C + D → 5 units + 4 units + 6 units + 5 units

http://www.kungfu-math.com/worksheets/grade5-ratio.html[26/1/2015 5:52:34 PM]

= 20 units 20 units = 20 x 6 cm 2

= 120 cm²

The area of the circle is 120 cm 2.