Year 7 - Area and perimeter - Free practice

Year 7 Area & Perimeter Worksheets

Rectangles, triangles, parallelograms - formulas and word problems.

Quick answer

How do you find the area and perimeter of rectangles, triangles and parallelograms?

Perimeter is the total distance around a shape. Area measures the space inside it. For rectangles, Area = length × width. For triangles, Area = ½ × base × height. For parallelograms, Area = base × height. For example, a triangle with base 8 cm and height 5 cm has area ½ × 8 × 5 = 20 cm².

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Worked examples

Year 7 area and perimeter: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Area of a triangle
Find the area of a triangle with a base of $8$ cm and a perpendicular height of $5$ cm.
Show worked solution
Key idea: The area of a triangle is $A = \dfrac{1}{2} \times b \times h$ , where $b$ is the base and $h$ is the perpendicular height.
1. Write the formula: $A = \frac{1}{2} \times b \times h$
2. Substitute $b = 8$ and $h = 5$ : $A = \frac{1}{2} \times 8 \times 5$
3. Calculate: $A = \frac{1}{2} \times 40 = 20$
Answer: The area of the triangle is $20$ cm².
Example 2 · Perimeter and area of a compound shape
A compound shape is made by joining a rectangle and a square. The rectangle is $10$ m long and $4$ m wide. The square has a side length of $4$ m and is attached to the right end of the rectangle, so the two shapes share one $4$ m edge. Find the total perimeter and total area of the compound shape.
Show worked solution
Key idea: For a compound shape, split it into simpler shapes to find the area, and trace the outside edges carefully to find the perimeter.
1. Find the area of the rectangle: $A_{\text{rect}} = 10 \times 4 = 40 \text{ m}^2$
2. Find the area of the square: $A_{\text{sq}} = 4 \times 4 = 16 \text{ m}^2$
3. Add the areas: $A_{\text{total}} = 40 + 16 = 56 \text{ m}^2$
4. Trace the outside edges. The overall shape is a rectangle $14$ m long and $4$ m wide (the shared edge is internal, not on the boundary): $P = 2 \times (14 + 4) = 2 \times 18 = 36 \text{ m}$
Answer: Total area $= 56$ m²; total perimeter $= 36$ m.
Example 3 · Fencing and floor area
Mia is setting up a vegetable garden in her backyard. The garden is in the shape of a parallelogram with a base of $6$ m and a perpendicular height of $3.5$ m. She also wants to put a fence all the way around the garden. The parallelogram has two sides of length $6$ m and two sides of length $4$ m. Fencing costs $12 per metre and soil costs $8 per square metre. How much will Mia spend in total?
Show worked solution
Key idea: Use the parallelogram area formula for the soil cost and the perimeter for the fencing cost, then add both costs.
1. Find the area of the garden: $A = b \times h = 6 \times 3.5 = 21 \text{ m}^2$
2. Find the perimeter of the garden: $P = 2 \times (6 + 4) = 2 \times 10 = 20 \text{ m}$
3. Calculate the cost of soil: $21 \times 8 = \$168$
4. Calculate the cost of fencing: $20 \times 12 = \$240$
5. Find the total cost: $168 + 240 = \$408$
Answer: Mia will spend $408 in total.

Common mistakes

Where students usually lose marks

Using slant height instead of perpendicular height

Triangle with base $6$ cm, slant side $5$ cm, perpendicular height $4$ cm: $A = \frac{1}{2} \times 6 \times 5 = 15$ cm²

Always use the perpendicular (right-angle) height in the formula $A = \frac{1}{2} \times b \times h$ , not the length of the slanted side. The perpendicular height is the straight-up measurement from the base to the top.

Forgetting the 1/2 in the triangle formula

Triangle with base $8$ cm, height $5$ cm: $A = 8 \times 5 = 40$ cm²

A triangle is exactly half of a rectangle with the same base and height, so you must always multiply by $\frac{1}{2}$ . The correct answer here is $\frac{1}{2} \times 8 \times 5 = 20$ cm².

Counting shared edges in the perimeter of a compound shape

Two $4$ m $\times$ $4$ m squares joined along one side: $P = 4 \times 4 + 4 \times 4 = 32$ m

The shared edge is inside the shape, so it is not part of the perimeter. Trace only the outer boundary of the compound shape to count the correct edges.

Mixing up perimeter and area

Finding how much carpet is needed for a room but calculating $P = 2 \times (5 + 3) = 16$ m instead of area

Perimeter measures the distance around the outside (used for fencing, edging). Area measures the surface inside (used for carpet, paint, tiles). Read the question carefully to decide which one you need.

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Your turn

A rectangular room is 7 m long and 4 m wide. What is the area of the room in square metres?

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About this worksheet

Why we built it

Year 7 students are expected to fluently calculate area and perimeter of rectangles, triangles and parallelograms, and apply those formulas to real-world problems. These worksheets give them mixed-shape practice every click so they can't just memorise one type.

What's covered

Sub-skills your student will practise

✓Perimeter of rectangles, squares and compound shapes
✓Area of a rectangle and square
✓Area of a triangle using base x height x 1/2
✓Area of parallelograms
✓Word problems involving floor area, paint, fencing

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Frequently asked

Questions parents ask about area and perimeter

What area and perimeter formulas does Year 7 require?

Rectangles (length x width), squares (side squared), triangles (half x base x height), and parallelograms (base x height). Year 8 builds on this with composite shapes and circles.

Why is the triangle area formula a half?

Because a triangle is exactly half a parallelogram with the same base and height - you can prove this by cutting a parallelogram diagonally. Most Year 7 students remember the formula but not why; the worksheets occasionally test the reasoning.

How do students handle parallelograms when the height isn't given?

The height must be perpendicular to the base, not the slanted side. This catches a lot of students who multiply the two visible side lengths instead of base x perpendicular height.

What units do answers need to be in?

Always include units. Area answers use squared units (cm^2, m^2). Perimeter uses linear units (cm, m). Marks are routinely deducted for missing or wrong units even when the number is correct.

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