Mensuration of 2 D Shapes

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Mensuration of 2-D Shapes Question Paper 1

Level IGCSE

Subject Maths

Exam Board Edexcel

Topic Shape, Space and Measures

Sub Topic Mensuration of 2-D Shapes

Booklet Question Paper 1

Time Allowed: 58 minutes

Score: /48

Percentage: /100

Grade Boundaries:

9 8 7 6 5 4 3

>90% 80% 70% 60% 50% 40% 30%

2 1

20% 10%

1 The perimeter of a triangle is 90 cm.The lengths of the sides of the triangle are in the ratios 3 : 5 : 7

Work out the length of the longest side of the triangle.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm

(Total for Question 1 is 3 marks)

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2 (a) Here is a shape made from a rectangle and a semicircle.

The length of the rectangle is 7.1 cm.The radius of the semicircle is 2.7 cm.

Work out the area of the shape.Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(4)

Diagram NOT accurately drawn

7.1 cm

2.7 cm

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(b) Here is another shape made from a rectangle and a semicircle.

The length of the rectangle is L cm.The radius of the semicircle is r cm.

The perimeter P, cm, of the shape is given by the formula

P = πr + 2L + 2r

Make r the subject of the formula P = πr + 2L + 2r.

r = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

(Total for Question 2 is 7 marks)

Diagram NOT accurately drawn

L cm

r cm

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3 The diagram shows a trapezium PQRS.

Q 6cm

8cm

5cm

Diagram NOTaccurately drawn

R

P S

(a) Calculate the area of the trapezium PQRS.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(2)

(b) Calculate the length PQ.Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm(4)

(Total for Question 3 is 6 marks)

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4

Diagram NOT accurately drawn

C

B

A9 cm

9 cm

35°D

O

AOD is a diameter of a circle, with centre O and radius 9 cm.ABC is an arc of the circle.AC is a chord.Angle ADC = 35°

Calculate the area of the shaded segment.Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(Total for Question 4 is 6 marks)

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5

ABCD is a rhombus.The diagonals AC and BD cross at the point E.AE CEBE DEAngle AEB

(a) Work out the area of the rhombus.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(3)

A

B

C

D

E6 cm

4 cm

4 cm

6 cm

Diagram NOT accurately drawn

(b) Work out the length of AB.Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm (3)

(Total for Question 5 is 6 marks)

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6

Diagram NOTaccurately drawn

NA B

CD

9 cm 5 cm

The shape ABCD is made from a rectangle ANCD and the right-angled triangle NBC. ANB is a straight line. AN = 9 cm. NB = 5 cm. The area of rectangle ANCD is 36 cm2

Work out the area of shape ABCD.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(Total for Question 6 is 4 marks)

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7 A circle has a diameter of 7.6 cm.Work out the circumference of the circle. Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm

(Total for Question 7 is 2 marks)

8 16 cm

4 cm

10 cm

Diagram NOT accurately drawn

9 cm

The diagram shows a shape.

Work out the area of the shape.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(Total for Question 8 is 4 marks)

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9 Here is a shape.

The shape is made from triangle ABC and a sector of a circle, centre C and radius CA.CA = 7 cm.CB = 16 cm.

Angle ACB���&�>X

Calculate the area of the shape.Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

B

&�>X7 cm

C

9 cm7 cm

A

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(Total for Question 9 is 6 marks)

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10 The diagram shows the path of an athlete on a running track.

The path consists of two straight lengths and a semicircle at each end.Each straight length is 85 metres.Each semicircle has a radius of 36.6 metres.

Calculate the area enclosed by the path.Give your answer correct to 3 significant figures.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2

(Total for Question 10 is 4 marks)

85 m

36.6 m

Diagram NOT accurately drawn

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