Planimonde at school

Scale, perimeter and area become concrete when students measure their own classroom and draw it. Students need no account.

Draw the classroom

In class

Students measure a real place (the classroom, the hallway, the yard) with a tape, in teams, and write down each side.
They type their measurements: the shape builds itself. Two diagonals are enough to draw a room whose angles are not square.
The plan shows the perimeter and the area: compare with the calculation done by hand and look for where the gap comes from.
The plan printed to scale is measured with a ruler: go from paper to reality, then from reality to paper.

Without an account, plans stay in the device's browser: nothing is collected about students.

Six printable exercises

Three for elementary cycle 3, three for secondary school. They touch on notions from the mathematics program: measuring lengths and surfaces, reading a plan and scale in elementary school; proportionality, area of decomposable figures, the Pythagorean relation, Heron's formula and similar figures in secondary school.

Exercise 1 · Elementary, cycle 3

The classroom on a sheet of paper

Your classroom is 8 m long and 6 m wide. You draw it at a scale of 1:50: 1 cm on the plan represents 50 cm in the classroom.

How many centimetres long is the classroom on the plan?
And how wide?
A desk measures 60 cm by 45 cm. What are its dimensions on the plan?
Does the plan fit on a sheet of 21.6 cm by 27.9 cm?

Exercise 2 · Elementary, cycle 3

The school garden

The school is setting up a rectangular vegetable garden of 4.5 m by 2 m.

What is the perimeter of the garden?
What is its area?
It is surrounded by a fence, leaving a 1 m gate. How many metres of fence are needed?
One bag of compost covers 2 m². How many bags must be bought?

Exercise 3 · Elementary, cycle 3

The hallway

On a plan at a scale of 1:100, the school hallway is 12.5 cm long and 2 cm wide.

What are the real dimensions of the hallway, in metres?
What is its real area?
It is covered with tiles of 50 cm by 50 cm. How many tiles are needed?

Exercise 4 · Secondary, cycle 1

The L-shaped yard

A yard has the shape of a 12 m by 8 m rectangle with one rectangular corner of 5 m by 3 m missing, taken up by a shed.

What is the area of the yard?
What is its perimeter? Compare it with that of the full rectangle.
Sod is laid in rolls of 0.6 m by 1.5 m. How many rolls are needed?
What are the overall dimensions of the yard on a plan at a scale of 1:100?

Exercise 5 · Secondary, cycle 2

The four-sided lot

A lot ABCD was measured with a tape: AB = 30 m, BC = 40 m, CD = 41 m, DA = 39 m. The diagonal AC measures 50 m. Nobody measured an angle.

Is angle B a right angle? Justify.
What is the area of triangle ABC?
What is the area of triangle ACD? Use Heron's formula.
What is the area of the lot, and what is its perimeter?

Exercise 6 · Secondary, cycle 2

Changing scale

On a plan at a scale of 1:200, a rectangular parking lot measures 15 cm by 9 cm.

What are its real dimensions?
What is its real area?
What is the ratio between the real area and the area on the plan? Compare it with the ratio of the lengths.
The plan is reprinted at a scale of 1:500. What are the new dimensions of the parking lot on paper?

Answer key

Exercise 1 · The classroom on a sheet of paper

8 m = 800 cm; 800 ÷ 50 = 16 cm.
6 m = 600 cm; 600 ÷ 50 = 12 cm.
60 ÷ 50 = 1.2 cm and 45 ÷ 50 = 0.9 cm.
Yes: 16 cm by 12 cm is smaller than the sheet.

Exercise 2 · The school garden

2 × (4.5 + 2) = 13 m.
4.5 × 2 = 9 m².
13 − 1 = 12 m.
9 ÷ 2 = 4.5: 5 bags are needed, since half a bag cannot be bought.

Exercise 3 · The hallway

12.5 × 100 = 1,250 cm = 12.5 m; 2 × 100 = 200 cm = 2 m.
12.5 × 2 = 25 m².
One tile covers 0.5 × 0.5 = 0.25 m²; 25 ÷ 0.25 = 100 tiles.

Exercise 4 · The L-shaped yard

12 × 8 − 5 × 3 = 96 − 15 = 81 m².
12 + 8 + 7 + 3 + 5 + 5 = 40 m, the same as the full rectangle: 2 × (12 + 8) = 40 m. Removing a corner moves two sides without changing their total length.
One roll covers 0.6 × 1.5 = 0.9 m²; 81 ÷ 0.9 = 90 rolls.
12 cm by 8 cm.

Exercise 5 · The four-sided lot

Yes: 30² + 40² = 900 + 1,600 = 2,500 = 50². By the converse of the Pythagorean relation, triangle ABC is right-angled at B.
30 × 40 ÷ 2 = 600 m².
Semi-perimeter: (50 + 41 + 39) ÷ 2 = 65. Area = √(65 × 15 × 24 × 26) = √608,400 = 780 m².
Area: 600 + 780 = 1,380 m². Perimeter: 30 + 40 + 41 + 39 = 150 m.

Exercise 6 · Changing scale

15 × 200 = 3,000 cm = 30 m; 9 × 200 = 1,800 cm = 18 m.
30 × 18 = 540 m².
Area on the plan: 15 × 9 = 135 cm². Real area: 540 m² = 5,400,000 cm². Ratio: 5,400,000 ÷ 135 = 40,000 = 200². The ratio of the areas is the square of the ratio of the lengths.
3,000 ÷ 500 = 6 cm and 1,800 ÷ 500 = 3.6 cm.

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