UK K12 GCSE/A-Level: Year 3 KS2 Mathematics - Measurement, Perimeter of Shapes

Learning Objectives

By the end of this topic, students will be able to:

• Define the perimeter of a shape and explain its importance in real-life situations.
• Calculate the perimeter of various shapes, including rectangles, squares, triangles, and circles.
• Identify and apply the formula for the perimeter of a rectangle (P = 2l + 2w).
• Use practical measurement skills to find the perimeter of shapes in different contexts.
• Recognize and explain the relationship between perimeter and other geometric properties, such as area and circumference.

Core Concepts

The perimeter of a shape is the distance around its edges. It is an essential concept in mathematics, as it is used to calculate the length of fencing required to enclose a garden, the amount of fabric needed to make a dress, or the length of wire needed to create a frame.

Types of Shapes

Different shapes have different perimeter formulas:

• Rectangle: P = 2l + 2w (where l is the length and w is the width)
• Square: P = 4s (where s is the side length)
• Triangle: P = a + b + c (where a, b, and c are the side lengths)
• Circle: P = 2?r (where r is the radius)

Units of Measurement

When calculating perimeter, it is essential to use the correct units of measurement. In the UK, the most common units for measuring length are meters (m), centimeters (cm), and millimeters (mm).

Worked Examples

Example 1: Rectangle

A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?

Using the formula P = 2l + 2w, we can substitute the values:

P = 2(8) + 2(5) P = 16 + 10 P = 26 cm

Example 2: Square

A square has a side length of 6 cm. What is its perimeter?

Using the formula P = 4s, we can substitute the value:

P = 4(6) P = 24 cm

Example 3: Triangle

A triangle has side lengths of 3 cm, 4 cm, and 5 cm. What is its perimeter?

Using the formula P = a + b + c, we can substitute the values:

P = 3 + 4 + 5 P = 12 cm

Common Misconceptions

• Students may confuse perimeter with area. Perimeter is the distance around a shape, while area is the amount of space inside a shape.
• Students may forget to use the correct units of measurement when calculating perimeter.
• Students may struggle to apply the formula for the perimeter of a rectangle (P = 2l + 2w) to more complex shapes.

Exam Tips

• Make sure to read the question carefully and understand what is being asked.
• Use the correct units of measurement when calculating perimeter.
• Apply the formula for the perimeter of a rectangle (P = 2l + 2w) to more complex shapes.
• Use practical measurement skills to find the perimeter of shapes in different contexts.

MCQs

MCQ 1: [F]

What is the perimeter of a rectangle with a length of 6 cm and a width of 4 cm?

A) 10 cm B) 12 cm C) 20 cm D) 24 cm

Correct answer: B) 12 cm Why the distractors fail: A) 10 cm is the perimeter of a square with a side length of 5 cm, not a rectangle. C) 20 cm is the perimeter of a rectangle with a length of 10 cm and a width of 2 cm. D) 24 cm is the perimeter of a rectangle with a length of 12 cm and a width of 2 cm.

MCQ 2: [H]

What is the perimeter of a triangle with side lengths of 7 cm, 8 cm, and 9 cm?

A) 12 cm B) 20 cm C) 24 cm D) 30 cm

Correct answer: D) 30 cm Why the distractors fail: A) 12 cm is the perimeter of a triangle with side lengths of 3 cm, 4 cm, and 5 cm. B) 20 cm is the perimeter of a triangle with side lengths of 5 cm, 6 cm, and 9 cm. C) 24 cm is the perimeter of a triangle with side lengths of 6 cm, 7 cm, and 11 cm.

MCQ 3: [F]

What is the perimeter of a square with a side length of 5 cm?

A) 10 cm B) 15 cm C) 20 cm D) 25 cm

Correct answer: B) 20 cm Why the distractors fail: A) 10 cm is the perimeter of a square with a side length of 5 cm, but this is not the correct calculation. C) 20 cm is the perimeter of a square with a side length of 10 cm. D) 25 cm is the perimeter of a square with a side length of 5 cm, but this is not the correct calculation.

MCQ 4: [H]

What is the perimeter of a rectangle with a length of 10 cm and a width of 6 cm?

A) 16 cm B) 20 cm C) 24 cm D) 30 cm

Correct answer: C) 24 cm Why the distractors fail: A) 16 cm is the perimeter of a rectangle with a length of 8 cm and a width of 2 cm. B) 20 cm is the perimeter of a rectangle with a length of 10 cm and a width of 2 cm. D) 30 cm is the perimeter of a rectangle with a length of 15 cm and a width of 3 cm.

MCQ 5: [F]

What is the perimeter of a circle with a radius of 4 cm?

A) 8 cm B) 12 cm C) 16 cm D) 20 cm

Correct answer: C) 16 cm Why the distractors fail: A) 8 cm is the circumference of a circle with a radius of 2 cm. B) 12 cm is the circumference of a circle with a radius of 3 cm. D) 20 cm is the circumference of a circle with a radius of 5 cm.

Short-answer questions

1. A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?

(Answer should be 26 cm)

1. A square has a side length of 6 cm. What is its perimeter?

(Answer should be 24 cm)

1. A triangle has side lengths of 3 cm, 4 cm, and 5 cm. What is its perimeter?

(Answer should be 12 cm)

1. A circle has a radius of 5 cm. What is its circumference?

(Answer should be 31.4 cm)

1. A rectangle has a length of 12 cm and a width of 8 cm. What is its perimeter?

(Answer should be 40 cm)