Area and perimeter Quiz (Grade 2)

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Topic:

Score: 0 / 10

Area and perimeter — Notes & Worked Examples Show / Hide

Explanation:

Perimeter is the total distance all the way around the outside of a 2D shape (add all side lengths, measured in cm or m). Area is the space inside the shape, measured in square units (cm² or m²): Rectangle Area = length × width, and Triangle Area = 12 × base × perpendicular height.

For a compound L-shape, work out any missing side lengths first, then split the shape into two non-overlapping rectangles to find the total area.

Example 1: Find the perimeter and area of this right-angled triangle.

• Perimeter: 8 + 5 + 9.4 = 22.4 cm

• Area: 12 × 8 × 5 = 20 cm² (ignore slanted 9.4 cm)

Example 2: Find the area and perimeter of this L-shape.

• Missing horizontal = 10 − 4 = 6 cm; vertical = 7 − 3 = 4 cm

• Area: (4 × 7) + (6 × 3) = 28 + 18 = 46 cm²

• Perimeter: 10 + 7 + 4 + 4 + 6 + 3 = 34 cm

One Page Guide (PDF) Area and perimeter Worksheets

Question 1

[2 marks]

Find the perimeter of the square

Worked Solution & Answer

4 × 12 = 48 cm B1

Answer: 48 cm cm

Question 2

[2 marks]

Find the perimeter and area of the rectangle

Worked Solution & Answer

(The area of a rectangle is length × width)
P = 2(8+5) = 26 cm, A = 8\times5 = 40 cm² B1

Answer: P = 26 cm, A = 40 cm²

Question 3

[2 marks]

The diagram shows a shape on a centimetre grid.

(a) Find the area of the shape. [1 mark]

cm²

(b) Find the perimeter of the shape. [1 mark]

Worked Solution & Answer

(a)

2×6 + 1×2 = 14 squares = 14 cm² B1

Answer (a): 14 cm²

(b)

2 + 4 + 1 + 2 + 3 + 6 = 18 cm B1

Answer (b): 18 cm

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Question 4

[4 marks]

Here are two rectangles.

QR = 10 cm
BC = PQ
The perimeter of ABCD is 26 cm
The area of PQRS is 45 cm²
Find the length of AB.

Worked Solution & Answer

PQ = 45 ÷ 10 = 4.5 cm ⇒ BC = 4.5 cm M3
Perimeter of ABCD = 2(AB + 4.5) = 26 ⇒ AB + 4.5 = 13 ⇒ AB = 8.5 cm A1

Answer: 8.5 cm

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Question 5 IGCSE Jan 2020 1FR Q8

[4 marks]

Here is a rectangle.

Work out the perimeter of the shape.

Worked Solution & Answer

(The area of a rectangle is length × width)
Length of one rectangle = 28 ÷ 4 = 7 cm M2
Exposed top vertical sides = 7 – 4 = 3 cm each M1
Perimeter = 7 + 4 + 7 + 3 + 4 + 3 + 7 + 4 + 7 + 4 = 50 cm A1

Answer: 50 cm

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Question 6

[4 marks]

The diagram shows a triangle and a rectangle.

The perimeter of the rectangle is a quarter of the perimeter of the triangle.
Work out the length of the rectangle.

Worked Solution & Answer

Triangle perimeter = 36 + 30 + 14 = 80 cm M2
Rectangle perimeter = 80 ÷ 4 = 20 cm M1
Length = (20 – 2 × 4) ÷ 2 = 6 cm A1

Answer: 6 cm

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Question 7

[4 marks]

Here are a triangle and a rectangle.

The area of the rectangle is 6 times the area of the triangle.
Work out the width of the rectangle.

Worked Solution & Answer

Area of triangle = ½ × 8 × 9 = 36 cm² M2
Area of rectangle = 6 × 36 = 216 cm² M1
Width = 216 ÷ 16 = 13.5 cm A1

Answer: 13.5 cm

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Question 8 OCR Nov 2019 3F Q22 / 6H Q4

[5 marks]

The diagram shows two rectangles, **A** and **B**.

Rectangle **A** has a width of 25 cm and a height of 12 cm.
The width of rectangle **B** is three times the height of rectangle **B**.
The area of rectangle **A** is equal to the area of rectangle **B**.
Find the perimeter of rectangle **B**.

Worked Solution & Answer

(The area of a rectangle is length × width)
Area of rectangle A = 25 × 12 = 300 cm² M2
Let height of rectangle B be h, so width = 3h M1
Area of rectangle B = 3h × h = 3h² = 300 ⇒ h² = 100 ⇒ h = 10 cm, width = 30 cm M1
Perimeter of rectangle B = 2 × (10 + 30) = 80 cm. A1

Answer: 80 cm

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Question 9

[5 marks]

A square has an area of 81 cm²

(a) Find the perimeter of the square. [2 marks]

(b) Find the value of h. [3 marks]

h =

Worked Solution & Answer

(a)

√81 = 9 cm M1
4 × 9 = 36 cm A1

Answer (a): 36 cm

(b)

(The area of a parallelogram is base × perpendicular height)
Area of triangle = 1/2 × 16 × 9 = 72 cm² M1
Area of parallelogram = 5 × 72 = 360 cm² M1
h = 360 ÷ 30 = 12 A1

Answer (b): h = 12

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Question 10 OCR Jun 2024 3F Q15

[8 marks]

In this question all measurements are in centimetres.
The shaded shape is made by cutting a square from the corner of a rectangle.

(a) Write down the relationship between the length and the width of the rectangle. [1 mark]

(b) Find an expression for the area of the shaded shape.
Give your answer in its simplest form. [2 marks]

(d) Find the value of k when the perimeter of the shaded shape is 62.4. [2 marks]

k =

Worked Solution & Answer

(a)

Length = 2k and width = k, so the length is double the width. C1

Answer (a): The length is twice the width.

(b)

(The area of a rectangle is length × width)
Area of rectangle = 2k × k = 2k² M1
area of square = g²
Shaded area = 2k² − g². A1

Answer (b): 2k² - g²

(c)

Perimeter = k + (2k − g) + g + g + (k − g) + 2k = 6k. M2 A1

Answer (c): 6k

(d)

6k = 62.4 M1
⇒ k = 62.4 ÷ 6 = 10.4. A1

Answer (d): k = 10.4

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Score: 0 / 10 (0 / 40 marks)

Area and perimeter Worksheets Next: Reading scales →

Grade 2 Quizzes

19 Topics

2A - Calculation problems	2B - Using a calculator
2C - Systematic listing	2D - Fraction of an amount
2E - FDP	2F - Simplifying algebra
2G - Writing an expression	2H - Function machines
2J - Solving one step equations	2K - Angles
2L - Area and perimeter	2M - Reading scales
2N - Probability & Probability Scale	2P - Frequency polygons
2Q - Unitary method	2R - Bar charts
2S - Pie charts	2T - Averages
2U - Stem and leaf diagrams