Perimeter and Area
Match Shapes to Perimeters (A)
Draw a line from each rectangle to its perimeter.
Match Shapes to Perimeters (B)
Draw a line from each rectangle to its perimeter.
Calculate the Perimeter (A)
Find the perimeter of each rectangle. Perimeter = 2 × (length + width).
Length = 8 cm, Width = 3 cm. Perimeter = ___
Length = 12 m, Width = 5 m. Perimeter = ___
Length = 15 cm, Width = 9 cm. Perimeter = ___
Calculate the Perimeter (B)
Find the perimeter of each rectangle.
Length = 20 m, Width = 8 m. Perimeter = ___
Length = 7.5 cm, Width = 4.5 cm. Perimeter = ___
Length = 25 m, Width = 10 m. Perimeter = ___
Quick Perimeter (A)
Circle the correct perimeter.
Square with sides of 6 cm
Rectangle 10 m × 4 m
Square with sides of 9 m
Rectangle 15 cm × 5 cm
Quick Perimeter (B)
Circle the correct perimeter.
Rectangle 11 m × 3 m
Square with sides of 12 cm
Rectangle 8 cm × 8 cm
Rectangle 20 m × 15 m
Perimeter Bonds
If you know the perimeter and one pair of sides, find the other pair. Half perimeter = L + W.
Sort by Perimeter
Calculate the perimeter and sort.
Calculate the Area (A)
Circle the correct area for each rectangle. Area = length × width.
6 m × 4 m
8 cm × 5 cm
10 m × 3 m
7 cm × 7 cm
Calculate the Area (B)
Circle the correct area.
12 m × 5 m
9 cm × 8 cm
15 m × 4 m
11 cm × 11 cm
Find the Area (A)
Calculate the area of each rectangle.
Length = 14 m, Width = 6 m. Area = ___ m²
Length = 9 cm, Width = 9 cm. Area = ___ cm²
Length = 20 m, Width = 8 m. Area = ___ m²
Length = 25 cm, Width = 4 cm. Area = ___ cm²
Find Both Perimeter and Area (A)
For each rectangle, calculate both the perimeter AND the area.
9 m × 6 m — Perimeter = ___ m, Area = ___ m²
11 cm × 4 cm — Perimeter = ___ cm, Area = ___ cm²
5 m × 5 m — Perimeter = ___ m, Area = ___ m²
Find Both Perimeter and Area (B)
Calculate both perimeter and area.
12 m × 8 m — Perimeter = ___ m, Area = ___ m²
7 cm × 10 cm — Perimeter = ___ cm, Area = ___ cm²
15 m × 3 m — Perimeter = ___ m, Area = ___ m²
Match Rectangles to Areas
Draw a line from each rectangle to its area.
Sort by Area
Calculate the area and sort.
Same Perimeter, Different Area
These rectangles all have a perimeter of 24 cm. Which has the largest area?
Which 24 cm perimeter rectangle has the largest area?
Which 20 m perimeter rectangle has the largest area?
Find the Missing Dimension
Use the given information to find the missing measurement.
Area = 48 m², Length = 8 m. Width = ___ m
Perimeter = 36 cm, Length = 12 cm. Width = ___ cm
Area = 100 cm², Width = 5 cm. Length = ___ cm
Perimeter = 50 m, Width = 10 m. Length = ___ m
Perimeter and Area Problems (A)
Solve each problem. Show your working.
A garden is 12 m long and 8 m wide. How much fencing is needed to go around it?
A classroom floor is 10 m × 7 m. How many square metres of carpet are needed?
A rectangle has a perimeter of 28 cm and a length of 9 cm. What is its width?
Perimeter and Area Problems (B)
Solve each problem.
A soccer field is 100 m × 60 m. What is its area? What is its perimeter?
A rectangular garden has an area of 72 m². The width is 6 m. What is the length? What is the perimeter?
Perimeter and Area Problems (C)
Solve these challenging problems.
You have 40 m of fencing. What is the largest rectangular area you can enclose? (Hint: try different lengths and widths that add to 20.)
A rectangular room is 5 m × 4 m. A rug 3 m × 2 m is placed in the middle. What area of floor is NOT covered by the rug?
Composite Shape Problems
Find the area by breaking the shape into rectangles.
An L-shaped room: one part is 6 m × 4 m, the other is 3 m × 2 m. What is the total area?
A T-shaped garden: the top bar is 8 m × 2 m, the stem is 2 m × 4 m. What is the total area?
Units for Perimeter and Area
Circle the correct unit.
Perimeter is measured in...
Area is measured in...
If sides are in metres, area is in...
A square has side 10 cm. Its area is 100...
Real-World Area Problems
Solve these real-world problems.
Paint covers 10 m² per litre. A wall is 5 m × 3 m. How many litres of paint are needed?
Tiles are 1 m × 1 m. A bathroom floor is 3 m × 2 m. How many tiles are needed?
Grass seed covers 5 m² per kilogram. A lawn is 20 m × 8 m. How many kg are needed?
Draw Rectangles with Given Measurements
Draw rectangles that match these descriptions.
Draw three different rectangles that all have an area of 24 cm². Write their dimensions.
Draw two rectangles with the same perimeter (20 cm) but different areas.
Perimeter Basics (A)
Circle the correct perimeter.
Rectangle: 5 cm × 3 cm
Square: side 4 cm
Rectangle: 10 m × 2 m
Square: side 7 m
Area Basics (A)
Circle the correct area.
Rectangle: 5 cm × 3 cm
Square: side 4 cm
Rectangle: 10 m × 2 m
Square: side 6 m
Calculate Perimeter (B)
Find the perimeter.
Rectangle: length 12 cm, width 5 cm. P = ___
Square: side 9 m. P = ___
Rectangle: length 20 m, width 8 m. P = ___
Rectangle: length 15 cm, width 15 cm. P = ___
Calculate Area (B)
Find the area.
Rectangle: length 12 cm, width 5 cm. A = ___
Square: side 9 m. A = ___
Rectangle: length 20 m, width 8 m. A = ___
Rectangle: 7 cm × 7 cm. A = ___
Perimeter Bonds
A rectangle's perimeter = 2(L + W). If the half-perimeter is the total, find the missing side.
Area Factor Pairs
A rectangle's area = L × W. Find the missing dimension.
Match Rectangles to Perimeters (B)
Draw a line.
Find the Missing Side — Perimeter (A)
Find the missing dimension.
Perimeter = 24 cm. Length = 8 cm. Width = ___
Perimeter = 36 m. Length = 12 m. Width = ___
Perimeter = 50 cm. Width = 10 cm. Length = ___
Find the Missing Side — Area (A)
Find the missing dimension.
Area = 40 cm². Length = 8 cm. Width = ___
Area = 72 m². Length = 9 m. Width = ___
Area = 100 cm². It's a square. Side = ___
Perimeter and Area Differences
Circle the correct answer.
Which measures the boundary?
Which is measured in square units?
Two rectangles with same perimeter always have same area.
A square with side 5 has P = 20 and A = 25.
Compare Perimeter and Area
Calculate both P and A.
Rectangle 6 × 4: P = ___. A = ___
Rectangle 8 × 2: P = ___. A = ___
Square 5 × 5: P = ___. A = ___
Which of the above has the largest area? ___
Sort: Greater Perimeter or Greater Area?
For each pair, sort which rectangle wins.
Perimeter Word Problems (A)
Solve.
A rectangular garden is 12 m long and 8 m wide. How much fencing is needed? ___
A square picture frame has a perimeter of 80 cm. What is the side length? ___
A room is 5 m × 4 m. How many metres of skirting board are needed? (subtract 1 m for the door)
Area Word Problems (A)
Solve.
A playground is 25 m × 15 m. What is its area? ___
A wall is 4 m × 3 m. Each tin of paint covers 6 m². How many tins needed? ___
A square patio has an area of 64 m². What is its side length? ___
Composite Shapes — Perimeter
Find the perimeter of L-shapes.
An L-shape made of two rectangles: 10 cm × 4 cm and 6 cm × 4 cm joined on a 4 cm side. Draw it and find the perimeter.
A shape is made from a 8 m × 5 m rectangle with a 3 m × 2 m rectangle cut from one corner. Find the perimeter.
Composite Shapes — Area
Find the area by splitting into rectangles.
An L-shape: split it into a 10 × 4 rectangle and a 6 × 4 rectangle. Total area: ___
A T-shape: top part 8 × 2, vertical part 2 × 6. Total area: ___
Perimeter and Area Challenge
Think carefully.
Can two rectangles have the same area but different perimeters? Give an example.
Can two rectangles have the same perimeter but different areas? Give an example.
For a fixed area of 36 cm², which rectangle has the smallest perimeter?
Area and Perimeter Reasoning
Circle the correct answer.
If you double the side of a square, the area...
If you double the side of a square, the perimeter...
The square with the largest area for a given perimeter has...
Match Area Formula to Shape
Draw a line.
Area Bonds (B)
Area = L × W. Find the missing dimension.
Perimeter or Area? (B)
Circle whether you'd use perimeter or area.
How much fence to go around a backyard?
How many tiles needed to cover a floor?
Length of border around a photo frame?
How much carpet for a room?
Sort Shapes by Area Size (Estimate)
Estimate which shape has the largest area.
Surface Area Introduction
Surface area is the sum of all face areas.
A cube has side length 4 cm. Area of one face: ___ cm². Surface area (6 faces): ___
A rectangular box is 5 cm × 3 cm × 2 cm. What are the dimensions of each face type? ___
Surface area of the box: ___
Scale Drawings
Use a scale to work out real dimensions.
A room on a scale drawing is 6 cm × 4 cm. Scale is 1 cm = 2 m. Real dimensions: ___
A corridor is 12 m long. At 1 cm = 3 m, how long on the drawing? ___
Draw a bedroom that is 4 m × 3 m to a scale of 1 cm = 1 m:
Square Area Sequences
These show areas of squares with side lengths 1, 2, 3, 4... Continue.
Garden Bed Areas
Each icon = 2 m². Area of each garden bed.
| Rose bed | |
| Vegie bed | |
| Herb bed | |
| Lawn |
Total garden area?
Which bed has the biggest area?
What percentage of the area is lawn?
If fencing costs $12/m, cost to fence a 10m × 8m garden?
Room Sizes in a Home
Room dimensions measured and sorted by area.
| Item | Tally | Total |
|---|---|---|
Under 10 m² | ||
10–20 m² | ||
20–30 m² | ||
Over 30 m² |
Compare Areas and Perimeters
Tick which shape has the larger value.
Rectangle 3×4 (area=12) vs rectangle 4×4 (area=16)
Rectangle 3×4 (perimeter=14) vs rectangle 4×4 (perimeter=16)
Maximising Area for a Fixed Perimeter
Explore shapes with the same perimeter.
Perimeter = 20 m. Complete the table: L=1,W=___,Area=___; L=2,W=___,Area=___; L=4,W=___,Area=___; L=5,W=___,Area=___
Which rectangle has the maximum area? ___
What type of shape gives the maximum area for any perimeter? ___
Area of Irregular Shapes
Estimate area by counting squares.
On grid paper, draw an irregular shape. Count the full squares: ___ Count the half squares: ___ Estimated area: ___
Explain why this is only an estimate:
Perimeter and Area in Architecture
Architects calculate perimeter and area constantly.
A room measures 4.5 m × 3.8 m. Area: ___. Perimeter: ___
Skirting board (runs along walls) costs $8/m. Cost to install in this room: ___
Floor tiles are 50 cm × 50 cm. How many tiles needed for the room? (round up) ___
Triangle Area (B)
Area of a triangle = base × height ÷ 2.
Triangle: base 8 cm, height 5 cm. Area: ___
Triangle: base 12 m, height 7 m. Area: ___
A right triangle has legs 6 cm and 8 cm. Area: ___ Hypotenuse ≈ ___ (Hint: use 3-4-5 or 6-8-10)
Perimeter Problem Solving (C)
Solve these perimeter problems.
A rectangle's perimeter is 48 cm. The length is 15 cm. Width: ___
A square's perimeter is 52 cm. Side length: ___. Area: ___
An equilateral triangle's perimeter is 39 m. Each side: ___
Area Word Problems (B)
Solve these area problems.
A garden is 12 m × 8 m. A pond takes up 6 m² in one corner. Remaining lawn area: ___
A path 2 m wide surrounds a 10 m × 6 m garden. Total area including path: ___. Path area only: ___
Perimeter and Area: Choose the Formula
Circle the correct formula.
Perimeter of a rectangle
Area of a square
Area of a triangle
Perimeter of an equilateral triangle with side s
Area and Perimeter Formulas (B)
Match each shape to its area formula.
Area Bonds (C)
Find the missing dimension.
Perimeter vs Area: Which Increased?
If you double the length of one side of a rectangle, which changes more?
Rectangle 4×3, then 8×3: Perimeter increases by how much?
Rectangle 4×3, then 8×3: Area doubles from 12 to...
Which changes more (relative to original)?
If you double both dimensions, area changes by factor...
Sort Shapes by Area (Smallest to Largest)
Estimate and sort.
Composite Shapes Area
Find the area of composite (combined) shapes.
An L-shape: 8 m × 6 m with a 3 m × 2 m rectangle removed from one corner. Area: ___
A cross shape made from two rectangles: 6 cm × 2 cm horizontal and 2 cm × 6 cm vertical (overlapping 2 cm²). Total area: ___
Perimeter and Fencing Problems (B)
Solve these real-world problems.
A rectangular park is 250 m × 180 m. Fencing costs $12 per metre. Total cost: ___
You have 80 m of fencing. What is the largest rectangular area you can enclose?
Area Sequences
Continue the pattern (area of increasing shapes).
Compare Areas (B)
Which shape has a larger area?
Rectangle 3×8 = 24 cm² vs triangle base 8, height 6 = 24 cm² — equal?
Square 5×5 = 25 cm² vs rectangle 6×4 = 24 cm² — which is bigger?
Room Sizes Survey
Estimate and tally room sizes.
| Item | Tally | Total |
|---|---|---|
Less than 10 m² | ||
10–20 m² | ||
21–40 m² | ||
More than 40 m² |
Maximum Area Investigation
Investigate which rectangle has the largest area for a fixed perimeter.
Perimeter = 24 cm. List 4 different rectangles and their areas: ___
Which gives the largest area? ___. What shape is it? ___
What does this tell us about the relationship between shapes and area?
Garden Plot Areas
Each icon = 4 m². Track plot sizes.
| Rose garden | |
| Vegetable patch | |
| Lawn | |
| Paved area |
Largest area?
Total garden area?
Difference between lawn and paved area?
What percentage is the vegetable patch?
Home Activity: Measure Your Space
Find perimeters and areas at home!
- 1Measure the length and width of a room. Calculate its perimeter and area.
- 2Find the area of the top of a table or desk. Would a 1 m² tablecloth cover it?
- 3Draw three different rectangles that all have an area of 24 cm². What are their dimensions?
- 4If you wanted to put a border around a picture that is 30 cm × 20 cm, how much border strip would you need?
Match Rectangles to Areas
Draw a line from each rectangle to its area.
Match Rectangles to Perimeters (C)
Draw a line from each rectangle to its perimeter.
Find the Perimeter (C)
Circle the correct perimeter.
Rectangle 7 m × 3 m
Square with side 9 cm
Rectangle 12 cm × 5 cm
Square with side 6 m
Find the Area (C)
Circle the correct area.
Rectangle 7 m × 4 m
Square with side 8 cm
Rectangle 11 cm × 3 cm
Square with side 10 m
Find the Missing Side — Perimeter (B)
Find the missing dimension.
Perimeter = 30 cm. Length = 9 cm. Width = ___
Perimeter = 44 m. Width = 8 m. Length = ___
Square with perimeter = 52 cm. Side = ___
Perimeter = 100 cm. Length = 35 cm. Width = ___
Find the Missing Side — Area (B)
Find the missing dimension.
Area = 56 cm². Length = 8 cm. Width = ___
Area = 90 m². Width = 9 m. Length = ___
Square with area = 49 cm². Side = ___
Area = 120 cm². Length = 15 cm. Width = ___
Perimeter of Squares
Perimeter = 4 × side length. Find the missing value.
Sort: Perimeter Greater or Less Than 30 cm?
Sort each rectangle.
Sort: Area Greater or Less Than 30 cm²?
Sort each rectangle.
Perimeter Word Problems (B)
Solve each problem.
A running track is a rectangle 100 m × 50 m. What is the perimeter? ___
A square basketball court has a perimeter of 88 m. What is the side length? ___
Fence costs $12 per metre. A yard is 15 m × 10 m. What is the total fencing cost? ___
Area Word Problems (B)
Solve each problem.
Carpet costs $25 per m². A room is 6 m × 5 m. What is the total cost? ___
A garden is 12 m × 8 m. A 3 m × 2 m pond takes up part of it. What area is left for plants? ___
How many 1 m² paving stones fit in a 9 m × 7 m courtyard? ___
Garden Areas
Use the picture graph of garden plot areas.
| Plot A | |
| Plot B | |
| Plot C | |
| Plot D |
Which plot has the largest area?
Total area of all plots?
How much larger is Plot B than Plot C?
What fraction of the total area is Plot A?
Perimeter Survey
Students measured rooms. Count results.
| Item | Tally | Total |
|---|---|---|
P < 20 m | ||
P = 20-30 m | ||
P = 30-40 m | ||
P > 40 m |
Which Has Greater Perimeter?
Compare the perimeters of each pair.
4×6 cm vs 3×6 cm: which has greater P?
5×7 vs 4×7: which has greater P?
6×8 vs 7×8: which has greater P?
Which Has Greater Area?
Compare the areas of each pair.
6×4 vs 5×4: which has greater area?
7×5 vs 8×4: which has greater area?
8×5 vs 9×4: which has greater area?
Different Dimensions, Same Area
Find rectangles with the given area.
Area = 24 cm². List 3 different rectangles: ___, ___, ___
Area = 36 cm². List 3 different rectangles: ___, ___, ___
Which rectangle with area 24 cm² has the smallest perimeter? ___
Different Dimensions, Same Perimeter
Find rectangles with perimeter 24 cm.
List 4 rectangles with perimeter = 24 cm: ___, ___, ___, ___
Calculate the area of each one: ___, ___, ___, ___
Which has the largest area? Is it the most square-like? ___
Composite Shapes — Perimeter (B)
Find the perimeter of each composite shape.
A cross shape: 3 rectangles. Top: 2×1, Centre: 6×2, Bottom: 2×1 cm. Find the perimeter.
A staircase shape: steps are 2 cm wide × 1 cm tall, 3 steps. Find the perimeter.
Composite Shapes — Area (B)
Find the area by splitting.
An L-shape: 8 m × 5 m rectangle with a 3 m × 2 m piece removed from one corner. Area = ___
A plus (+) shape: centre 3×3, four arms each 1×2. Area = ___
Area and Perimeter Mixed Quiz
Circle the correct answer.
P of square with side 7 cm = ?
A of rectangle 6 cm × 9 cm = ?
Side of square with A = 36 cm² = ?
Width of rectangle with A=48 cm² and L=8 cm = ?
Area Sequences
Find the pattern and fill in the missing area.
Scale Drawing Areas
Use scale to find real areas.
Scale: 1 cm = 5 m. A room measures 4 cm × 3 cm on the drawing. Real dimensions: ___ × ___. Real area: ___
Scale: 1 cm = 10 m. A field is 3 cm × 5 cm on a map. Real area: ___
Perimeter and Area Investigation
Investigate the relationship between perimeter and area.
If you double both dimensions of a rectangle, what happens to the perimeter? ___
If you double both dimensions, what happens to the area? ___
Which shape — square or rectangle — gives the largest area for a given perimeter? ___