Measurement & Geometry — Worked Solutions (Year 7 Maths)
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Worked examples for Year 7 Maths Measurement & Geometry. Each shows where the marks are awarded, the key idea, and the full solution explained by your choice of tutor — Stella, Ella or Cassie.
In short: full step-by-step worked solutions for Year 7 Maths — Measurement & Geometry. Every question is worked through with the method and reasoning shown, so you can check how to get the answer, not just the final result.
How to use these
Try each question first, then check your working. Use the tutor tabs to read the full solution in the style that suits you: Stella is direct and challenging, Ella is warm and explains the why, and Cassie is concise and analytical.
Example 1 — Area and perimeter of an L-shape
Question
A rectangular garden bed is 8 m long and 5 m wide. A small square section measuring 2 m by 2 m is removed from one corner. Find the area of the remaining garden bed.
Solution
Find the full rectangle, then take away the square.
Rectangle area: $8 \times 5 = 40 \text{ m}^2$.
Square removed: $2 \times 2 = 4 \text{ m}^2$.
Remaining area: $40 - 4 = 36 \text{ m}^2$.
The answer is $36 \text{ m}^2$. Always keep the units squared for area — drop them and you lose an easy mark.
The trick with an awkward shape is to start with a shape you already know, then adjust. Here we have a full rectangle with a corner taken out.
First the whole rectangle. Area of a rectangle is length times width, so $8 \times 5 = 40 \text{ m}^2$.
The piece removed is a square 2 m on each side, so its area is $2 \times 2 = 4 \text{ m}^2$.
Because that square is gone, we subtract it from the rectangle: $40 - 4 = 36 \text{ m}^2$.
So the remaining garden bed is $36 \text{ m}^2$. We write $\text{m}^2$ because area measures a flat surface in two directions, length and width together.
Whole minus removed piece.
- Rectangle: $8 \times 5 = 40 \text{ m}^2$
- Square removed: $2 \times 2 = 4 \text{ m}^2$
- Remaining: $40 - 4 = 36 \text{ m}^2$
Answer: $36 \text{ m}^2$.
Where the marks go
- 1 mark: Correct rectangle area: $8 \times 5 = 40 \text{ m}^2$
- 1 mark: Correct area of the removed square: $2 \times 2 = 4 \text{ m}^2$
- 1 mark: Correct remaining area with units: $36 \text{ m}^2$
Key idea
For a composite shape, find the area of the whole rectangle and subtract any piece removed; keep area in square units.
Example 2 — Angles on a straight line
Question
Three angles meet at a point on a straight line. They measure $x$, $48^\circ$ and $77^\circ$. Find the value of $x$.
Solution
Angles on a straight line add to $180^\circ$, so write the equation and solve.
$x + 48 + 77 = 180$.
Add the known angles: $48 + 77 = 125$, so $x + 125 = 180$.
Subtract: $x = 180 - 125 = 55^\circ$.
So $x = 55^\circ$. State the reason "angles on a straight line sum to $180^\circ$" — the reason is part of the mark.
When angles sit side by side along a straight line, they fill a half-turn, which is $180^\circ$. So all three angles together must add to $180^\circ$.
That gives us $x + 48 + 77 = 180$.
Let's tidy the numbers we know: $48 + 77 = 125$. Now the equation is $x + 125 = 180$.
To find $x$ we take away the $125$: $x = 180 - 125 = 55^\circ$.
So $x = 55^\circ$. The whole idea rests on a straight line being a half-turn, which is why the three angles must total $180^\circ$.
Angles on a straight line sum to $180^\circ$.
- $x + 48 + 77 = 180$
- $48 + 77 = 125$
- $x = 180 - 125 = 55^\circ$
Answer: $x = 55^\circ$.
Where the marks go
- 1 mark: Sets up the equation $x + 48 + 77 = 180$ (angles on a straight line)
- 1 mark: Solves correctly to get $x = 55^\circ$
Key idea
Angles on a straight line add to $180^\circ$, so subtract the known angles from $180^\circ$ to find the unknown.
Frequently asked questions
Step-by-step solutions to Measurement & Geometry questions in Year 7 Maths, with the full method shown for each — so you can follow the reasoning, not just the final answer.
Attempt each question yourself first, then compare your method — not just your answer — against the worked solution. The aim is to learn the approach so you can handle unfamiliar questions, rather than memorising answers.
Yes — they follow the NESA syllabus for Year 7 Maths, using the methods and notation expected in exams and assessments.