Introduction

Hello, Year 5! Today, we are going to explore how to find the missing lengths of sides in shapes. This is an important skill in Maths, and I am excited to help you learn it!

Understanding Shapes

Shapes can have different lengths for their sides. Sometimes, we know the length of some sides, but we need to find out the length of others. Let’s look at some basic shapes:

  • Rectangle: A shape with 4 sides, where opposite sides are equal.
  • Square: A special type of rectangle where all sides are equal.
  • Triangle: A shape with 3 sides.

Key Rules

  1. For Rectangles:
    • Opposite sides are equal.
    • If one side is 5 cm, the opposite side is also 5 cm.
  2. For Squares:
    • All sides are equal.
    • If one side is 4 cm, all sides are 4 cm.
  3. For Triangles:
    • The lengths of the sides can be different.
    • To find a missing side, we might use the other two sides.

How to Find Missing Lengths

  1. Using Addition: Sometimes, you can find a missing length by adding two known lengths together.
    • Example: If the perimeter of a rectangle is 20 cm and one side is 6 cm, the other side can be found by subtracting:
    \text{Missing Side} = \text{Perimeter} – 2 \times \text{Known Side}
    \text{Missing Side} = 20 – 2 \times 6 = 20 – 12 = 8 \text{ cm}
  2. Using Subtraction: If you know the total length and some parts, you can subtract to find the missing length.
    • Example: If you have a line that is 10 cm long and 3 cm is already used, then the missing length is:
    \text{Missing Length} = 10 – 3 = 7 \text{ cm}

Tips and Tricks

  • Draw a Picture: Visualising the shape can help you see what you have and what you need to find.
  • Label Your Sides: Write down the lengths you know next to the sides of the shape.
  • Check Your Work: After finding a missing length, go back and see if it fits with the other sides.

Practice Questions

Easy Level Questions

  1. A rectangle has one side of 4 cm and the opposite side is missing. What is the missing side?
  2. A square has a side measuring 5 cm. What is the length of each side?
  3. A triangle has two sides measuring 3 cm and 4 cm. What is the missing side if the perimeter is 12 cm?
  4. A rectangle has a length of 8 cm and a width of 5 cm. What is the width?
  5. A square has a side measuring 6 cm. What is the total perimeter?
  6. A rectangle has one side of 10 cm. What is the length of the opposite side?
  7. A triangle has sides of 5 cm and 7 cm. What is the missing side if the perimeter is 20 cm?
  8. A square has a perimeter of 32 cm. What is the length of each side?
  9. A rectangle has a length of 9 cm. What is the missing width if the perimeter is 36 cm?
  10. A triangle has a base of 6 cm and a height of 8 cm. What is the missing length if the perimeter is 30 cm?

Medium Level Questions

  1. A rectangle has a length of 12 cm and a width that is double the length. What is the width?
  2. A triangle has sides measuring 10 cm and 14 cm. If the third side is missing, and the perimeter is 50 cm, what is the length of the missing side?
  3. A square has an area of 49 cm². What is the length of each side?
  4. A rectangle has a perimeter of 40 cm. If one side is 10 cm, what is the length of the opposite side?
  5. A triangle has two sides measuring 8 cm and 6 cm. What is the missing side if the perimeter is 30 cm?
  6. A square has a perimeter of 24 cm. What is the length of each side?
  7. A rectangle has one side measuring 15 cm. If the other side is 10 cm, what is the perimeter?
  8. A triangle has two sides measuring 5 cm and 12 cm. If the perimeter is 30 cm, what is the missing side?
  9. A rectangle has a length of 20 cm. If the perimeter is 60 cm, what is the width?
  10. A triangle has sides measuring 9 cm and 12 cm. If the third side is missing and the perimeter is 40 cm, what is the length of the third side?

Hard Level Questions

  1. A rectangle has a length of 25 cm and a perimeter of 100 cm. What is the width?
  2. A triangle has sides measuring 10 cm, 15 cm, and a missing side. If the perimeter is 60 cm, what is the missing side?
  3. A square has a diagonal of 14 cm. What is the length of each side?
  4. A rectangle has a length that is three times the width. If the perimeter is 64 cm, what are the dimensions?
  5. A triangle has two sides measuring 8 cm and 10 cm. If the perimeter is 40 cm, what is the missing side?
  6. A square has an area of 144 cm². What is the length of each side?
  7. A rectangle has a width of 6 cm and a perimeter of 30 cm. What is the length?
  8. A triangle has sides measuring 10 cm, 10 cm, and a missing side. If the perimeter is 40 cm, what is the missing side?
  9. A rectangle has a length of 18 cm and a width of 12 cm. What is the perimeter?
  10. A triangle has two sides measuring 7 cm and 9 cm. If the perimeter is 40 cm, what is the missing side?

Answers and Explanations

Easy Level Answers

  1. 4 cm
  2. 5 cm
  3. 5 cm
  4. 5 cm
  5. 24 cm
  6. 10 cm
  7. 8 cm
  8. 8 cm
  9. 8 cm
  10. 16 cm

Medium Level Answers

  1. 12 cm
  2. 26 cm
  3. 7 cm
  4. 10 cm
  5. 16 cm
  6. 6 cm
  7. 50 cm
  8. 13 cm
  9. 10 cm
  10. 9 cm

Hard Level Answers

  1. 25 cm
  2. 35 cm
  3. 10 cm
  4. Length = 12 cm, Width = 4 cm
  5. 22 cm
  6. 12 cm
  7. 9 cm
  8. 20 cm
  9. 60 cm
  10. 24 cm

I hope you found this lesson helpful! Remember to practice these types of questions, and soon you’ll be a pro at finding missing lengths!