Sec 1 Maths Perimeter and area worksheet with answers

A free Sec 1 Maths worksheet on perimeter and area: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 Maths worksheet: Perimeter and area

Total: 30 marksSuggested time: 45 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

In the diagram,

ABCD

is a parallelogram. The dashed line is perpendicular to

AB

. Find the area of

ABCD

Answerm²[2]

A rectangular window has an area of

0.55

m². Express this area in cm².

Answercm²[2]

A circle has a circumference of

34\pi

cm. Find its radius,

r

Answercm[2]

The diagram shows a circular fountain. Its radius is

11

m. Find its circumference, leaving your answer in terms of

\pi

Answerm[2]

Two identical circles fit exactly inside a rectangle of length

16

cm, as shown. Find the area of the shaded region, correct to 3 significant figures.

Answercm²[3]

Section B

(a)The diagram shows a circle. Its diameter is

12

m. Find its area, leaving your answer in terms of

\pi

Answer (a)m²[2]

(b)In the diagram,

ABCD

is a trapezium with

AB

parallel to

DC

. The dashed line is perpendicular to

AB

. Find the area of

ABCD

Answer (b)m²[2]

(a)The diagram shows a round pizza. Its diameter is

50

cm. Find its area, leaving your answer in terms of

\pi

Answer (a)cm²[2]

(b)A running track is made up of two straight sections and two semicircles, as shown. Find the perimeter of the track, correct to 3 significant figures.

Answer (b)cm[2]

(c)The floor of a kitchen is a rectangle measuring

2.4

m by

1.2

m. It is covered completely with square tiles of side

40

cm. Find the number of tiles needed.

Answer (c)[3]

(a)The diagram shows triangle

ABC

. Find its perimeter.

Answer (a)m[1]

(b)The diagram shows a hexagon made of two identical trapeziums joined along their longer parallel sides (the dashed line). The longer parallel side of each trapezium is

14

m and each trapezium is

6

m high. The area of the hexagon is

120

m². Find the value of

x

Answer (b)m[3]

(c)(i)Express

1.75

m² in cm².

Answer (c)(i)cm²[2]

(c)(ii)A classroom whiteboard has an area of

3.6

m². Express this area in cm².

Answer (c)(ii)cm²[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 96

m²[2]

\text{Area of } ABCD = \text{base} \times \text{height}

= 12 \times 8

= 96

m²

Question 2

Answer:

= 5500

cm²[2]

1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}

= 10\,000 \text{ cm}^2

0.55 \text{ m}^2 = 0.55 \times 10\,000 \text{ cm}^2

= 5500

cm²

Question 3

Answer:

= 17

cm[2]

2\pi r = 34\pi

r = \dfrac{34}{2}

= 17

Question 4

Answer:

= 22\pi

m[2]

C = 2\pi r

= 2\pi(11)

= 22\pi

Question 5

Answer:

= 27.5

cm² (3 s.f.)[3]

\text{Diameter} = \dfrac{16}{2}

= 8

r = 4

\text{The rectangle is } 16 \text{ by } 8

\text{Area} = 16 \times 8 - 2 \times \pi(4)^2

= 27.4690\ldots

= 27.5

cm² (3 s.f.)

Question 6

(a)Answer:

= 36\pi

m²[2]

r = \dfrac{12}{2}

= 6

A = \pi r^2

= \pi(6)^2

= 36\pi

m²

(b)Answer:

= 128

m²[2]

\text{Area of } ABCD = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}

= \dfrac{1}{2} \times (6 + 26) \times 8

= 128

m²

Question 7

(a)Answer:

= 625\pi

cm²[2]

r = \dfrac{50}{2}

= 25

A = \pi r^2

= \pi(25)^2

= 625\pi

cm²

(b)Answer:

= 61.4

cm (3 s.f.)[2]

\text{Curved parts} = \pi d

= \pi(10)

\text{Perimeter} = 15 + 15 + \pi(10)

= 61.4159\ldots

= 61.4

cm (3 s.f.)

(c)Answer:

= 18

[3]

2.4 \text{ m} = 240 \text{ cm}

1.2 \text{ m} = 120 \text{ cm}

\dfrac{240}{40} = 6

tiles along the length

\dfrac{120}{40} = 3

tiles along the breadth

\text{Number of tiles} = 6 \times 3

= 18

Question 8

(a)Answer:

= 70

m[1]

\text{Perimeter} = 28 + 25 + 17

= 70

(b)Answer:

x = 6

m[3]

\text{One trapezium} = \dfrac{120}{2}

\phantom{\text{One trapezium}} = 60

m²

\dfrac{1}{2} \times (x + 14) \times 6 = 60

x + 14 = \dfrac{2 \times 60}{6}

\phantom{x + 14} = 20

x = 6

(c)(i)Answer:

= 17\,500

cm²[2]

1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}

= 10\,000 \text{ cm}^2

1.75 \text{ m}^2 = 1.75 \times 10\,000 \text{ cm}^2

= 17\,500

cm²

(c)(ii)Answer:

= 36\,000

cm²[2]

1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}

= 10\,000 \text{ cm}^2

3.6 \text{ m}^2 = 3.6 \times 10\,000 \text{ cm}^2

= 36\,000

cm²

Practice questions by skill

Sec 1 Maths Perimeter and area worksheet with answers

In the print window, choose Save as PDF to download it.

Need the formulas first? Read the Perimeter and area notes. Or practise it online with step-by-step help when you get one wrong.

Section B

(a)The diagram shows a circle. Its diameter is

12

m. Find its area, leaving your answer in terms of

\pi

Answer (a)m²[2]

(b)In the diagram,

ABCD

is a trapezium with

AB

parallel to

DC

. The dashed line is perpendicular to

AB

. Find the area of

ABCD

Answer (b)m²[2]

Answers and worked solutions

Question 1

Answer:

= 96

m²[2]

\text{Area of } ABCD = \text{base} \times \text{height}

= 12 \times 8

= 96

m²

Question 2

Answer:

= 5500

cm²[2]

1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}

= 10\,000 \text{ cm}^2

0.55 \text{ m}^2 = 0.55 \times 10\,000 \text{ cm}^2

= 5500

cm²

Question 3

Answer:

= 17

cm[2]

2\pi r = 34\pi

r = \dfrac{34}{2}

= 17

Question 4

Answer:

= 22\pi

m[2]

C = 2\pi r

= 2\pi(11)

= 22\pi

Question 5

Answer:

= 27.5

cm² (3 s.f.)[3]

\text{Diameter} = \dfrac{16}{2}

= 8

r = 4

\text{The rectangle is } 16 \text{ by } 8

\text{Area} = 16 \times 8 - 2 \times \pi(4)^2

= 27.4690\ldots

= 27.5

cm² (3 s.f.)

Question 6

(a)Answer:

= 36\pi

m²[2]

r = \dfrac{12}{2}

= 6

A = \pi r^2

= \pi(6)^2

= 36\pi

m²

(b)Answer:

= 128

m²[2]

\text{Area of } ABCD = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}

= \dfrac{1}{2} \times (6 + 26) \times 8

= 128

m²

Question 7

(a)Answer:

= 625\pi

cm²[2]

r = \dfrac{50}{2}

= 25

A = \pi r^2

= \pi(25)^2

= 625\pi

cm²

(b)Answer:

= 61.4

cm (3 s.f.)[2]

\text{Curved parts} = \pi d

= \pi(10)

\text{Perimeter} = 15 + 15 + \pi(10)

= 61.4159\ldots

= 61.4

cm (3 s.f.)

(c)Answer:

= 18

[3]

2.4 \text{ m} = 240 \text{ cm}

1.2 \text{ m} = 120 \text{ cm}

\dfrac{240}{40} = 6

tiles along the length

\dfrac{120}{40} = 3

tiles along the breadth

\text{Number of tiles} = 6 \times 3

= 18

Question 8

(a)Answer:

= 70

m[1]

\text{Perimeter} = 28 + 25 + 17

= 70

(b)Answer:

x = 6

m[3]

\text{One trapezium} = \dfrac{120}{2}

\phantom{\text{One trapezium}} = 60

m²

\dfrac{1}{2} \times (x + 14) \times 6 = 60

x + 14 = \dfrac{2 \times 60}{6}

\phantom{x + 14} = 20

x = 6

(c)(i)Answer:

= 17\,500

cm²[2]

1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}

= 10\,000 \text{ cm}^2

1.75 \text{ m}^2 = 1.75 \times 10\,000 \text{ cm}^2

= 17\,500

cm²

(c)(ii)Answer:

= 36\,000

cm²[2]

1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}

= 10\,000 \text{ cm}^2

3.6 \text{ m}^2 = 3.6 \times 10\,000 \text{ cm}^2

= 36\,000

cm²