Sec 1 G2 Maths Perimeter and area worksheet with answers

A free Sec 1 G2 Maths worksheet on perimeter and area: 7 questions, 29 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 G2 Maths worksheet: Perimeter and area

Total: 29 marksSuggested time: 50 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,

ABC

is a triangle. The dashed line is perpendicular to

AB

. Find the area of triangle

ABC

Answerm²[2]

The diagram shows a figure made up of rectangles. All the corners are right angles. Find its area.

Answercm²[2]

(a)A classroom whiteboard has an area of

3.6

m². Express this area in cm².

Answer (a)cm²[2]

(b)A housing estate has an area of

1.25

ha. Express this area in m². (1 hectare

= 10\,000

m²)

Answer (b)m²[1]

The wheel of a bicycle has a diameter of

63

cm. Find the number of complete turns it makes when it travels

250

Answer[3]

Section B

(a)The diagram shows the trapezium

ABCD

, with

AB

parallel to

DC

. Find its perimeter.

Answer (a)cm[1]

(b)The figure is made up of a rectangle and a semicircle. Find its area, correct to 3 significant figures.

Answer (b)cm²[2]

(c)The diagram shows a rectangular carpet measuring

6

m by

75

cm. Find its area, in m².

Answer (c)m²[2]

(a)The diagram shows a figure made up of rectangles. All the corners are right angles. Find its perimeter.

Answer (a)m[2]

(b)In the diagram,

ABCD

is a parallelogram. The dashed lines are perpendicular to

AB

and to

AD

. Find the value of

x

Answer (b)m[2]

(c)The diagram shows a semicircle of diameter

28

cm. Find its perimeter, correct to 3 significant figures.

Answer (c)cm[3]

(a)In the diagram,

ABCD

is a parallelogram. The dashed line is perpendicular to

AB

. Find the area of

ABCD

Answer (a)m²[2]

(b)Express

4800

cm² in m².

Answer (b)m²[2]

(c)The diagram shows a circle of diameter

4.8

cm. Using the

\pi

key on your calculator, find the circumference of the circle, correct to 3 significant figures.

Answer (c)cm[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 63

m²[2]

\text{Area of } \triangle ABC = \dfrac{1}{2} \times \text{base} \times \text{height}

= \dfrac{1}{2} \times 21 \times 6

= 63

m²

Question 2

Answer:

= 96

cm²[2]

\text{Missing side} = 12 - 6

= 6

\text{Area} = 6 \times 10 + 6 \times 6

= 96

cm²

Question 3

(a)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

(b)Answer:

= 12\,500

m²[1]

1.25 \text{ha} = 1.25 \times 10\,000 \text{m}^2

= 12\,500

m²

Question 4

Answer: It makes

126

complete turns.[3]

\text{Circumference} = \pi d

= \pi(63)

= 197.9203\ldots

250 \text{ m} = 25000 \text{ cm}

\text{Turns} = \dfrac{25000}{\pi(63)}

= 126.3134\ldots

It makes

126

complete turns.

Question 5

(a)Answer:

= 50

cm[1]

\text{Perimeter} = 23 + 10 + 7 + 10

= 50

(b)Answer:

= 279

cm² (3 s.f.)[2]

r = \dfrac{10}{2}

= 5

\text{Area} = 24 \times 10 + \dfrac{1}{2} \times \pi(5)^2

= 279.2699\ldots

= 279

cm² (3 s.f.)

(c)Answer:

= 4.5

m²[2]

75 \text{ cm} = 75 \div 100 \text{ m}

= 0.75 \text{ m}

\text{Area} = 6 \times 0.75

= 4.5

m²

Question 6

(a)Answer:

= 54

m[2]

\text{Gap} = 12 - 4 - 4

= 4

\text{Both sides of the gap are } 5

\text{Perimeter} = 12 + 10 + 4 + 5 + 4 + 5 + 4 + 10

= 54

(b)Answer:

x = 8

m[2]

\text{Area} = 10 \times 12

= 120

m²

15x = 120

x = \dfrac{120}{15}

x = 8

(c)Answer:

= 72.0

cm (3 s.f.)[3]

r = \dfrac{28}{2}

= 14

\text{Arc} = \dfrac{1}{2} \times 2\pi(14)

= 43.9822\ldots

\text{Perimeter} = \dfrac{1}{2} \times 2\pi(14) + 14 + 14

= 71.9822\ldots

= 72.0

cm (3 s.f.)

Question 7

(a)Answer:

= 135

m²[2]

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

= 9 \times 15

= 135

m²

(b)Answer:

= 0.48

m²[2]

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

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

4800 \text{ cm}^2 = \dfrac{4800}{10\,000} \text{ m}^2

= 0.48

m²

(c)Answer:

= 15.1

cm (3 s.f.)[3]

r = \dfrac{4.8}{2}

= 2.4

C = 2\pi r

= 2\pi(2.4)

= 15.0796\ldots

= 15.1

cm (3 s.f.)

Sec 1 G2 Maths Perimeter and area worksheet with answers

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

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)The diagram shows the trapezium

ABCD

, with

AB

parallel to

DC

. Find its perimeter.

Answer (a)cm[1]

(b)The figure is made up of a rectangle and a semicircle. Find its area, correct to 3 significant figures.

Answer (b)cm²[2]

(c)The diagram shows a rectangular carpet measuring

6

m by

75

cm. Find its area, in m².

Answer (c)m²[2]

Answers and worked solutions

Question 1

Answer:

= 63

m²[2]

\text{Area of } \triangle ABC = \dfrac{1}{2} \times \text{base} \times \text{height}

= \dfrac{1}{2} \times 21 \times 6

= 63

m²

Question 2

Answer:

= 96

cm²[2]

\text{Missing side} = 12 - 6

= 6

\text{Area} = 6 \times 10 + 6 \times 6

= 96

cm²

Question 3

(a)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

(b)Answer:

= 12\,500

m²[1]

1.25 \text{ha} = 1.25 \times 10\,000 \text{m}^2

= 12\,500

m²

Question 4

Answer: It makes

126

complete turns.[3]

\text{Circumference} = \pi d

= \pi(63)

= 197.9203\ldots

250 \text{ m} = 25000 \text{ cm}

\text{Turns} = \dfrac{25000}{\pi(63)}

= 126.3134\ldots

It makes

126

complete turns.

Question 5

(a)Answer:

= 50

cm[1]

\text{Perimeter} = 23 + 10 + 7 + 10

= 50

(b)Answer:

= 279

cm² (3 s.f.)[2]

r = \dfrac{10}{2}

= 5

\text{Area} = 24 \times 10 + \dfrac{1}{2} \times \pi(5)^2

= 279.2699\ldots

= 279

cm² (3 s.f.)

(c)Answer:

= 4.5

m²[2]

75 \text{ cm} = 75 \div 100 \text{ m}

= 0.75 \text{ m}

\text{Area} = 6 \times 0.75

= 4.5

m²

Question 6

(a)Answer:

= 54

m[2]

\text{Gap} = 12 - 4 - 4

= 4

\text{Both sides of the gap are } 5

\text{Perimeter} = 12 + 10 + 4 + 5 + 4 + 5 + 4 + 10

= 54

(b)Answer:

x = 8

m[2]

\text{Area} = 10 \times 12

= 120

m²

15x = 120

x = \dfrac{120}{15}

x = 8

(c)Answer:

= 72.0

cm (3 s.f.)[3]

r = \dfrac{28}{2}

= 14

\text{Arc} = \dfrac{1}{2} \times 2\pi(14)

= 43.9822\ldots

\text{Perimeter} = \dfrac{1}{2} \times 2\pi(14) + 14 + 14

= 71.9822\ldots

= 72.0

cm (3 s.f.)

Question 7

(a)Answer:

= 135

m²[2]

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

= 9 \times 15

= 135

m²

(b)Answer:

= 0.48

m²[2]

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

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

4800 \text{ cm}^2 = \dfrac{4800}{10\,000} \text{ m}^2

= 0.48

m²

(c)Answer:

= 15.1

cm (3 s.f.)[3]

r = \dfrac{4.8}{2}

= 2.4

C = 2\pi r

= 2\pi(2.4)

= 15.0796\ldots

= 15.1

cm (3 s.f.)