vmbo havo vwo
Area calculator
Quick answer
Rectangle: A = l × b. Triangle: A = ½ × base × height. Circle: A = π r².
Examples: 4 × 5 = 20 cm²; ½ × 6 × 3 = 9 cm²; r = 2 gives 4π ≈ 12.5664 cm². Diameter: first r = d ÷ 2.
Calculator
Choose rectangle, triangle, circle, trapezium or parallelogram. cm, m or mm is a label only; we do not convert between units. The answer gets ² after the unit. Lengths must be greater than 0.
What is area?
Dutch school books say oppervlakte for what English calls area: how large a flat shape is. You count how many 1 cm × 1 cm squares fit inside; that is why the unit is cm² (or m², mm²). Length is a line; area is a plane; volume (Dutch: inhoud) is a solid — three different quantities. This page computes area only. How much fits inside is on the volume calculator (cube, sphere, cone) and the cylinder volume calculator.
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = l × b | 4 cm × 5 cm = 20 cm² |
| Triangle | A = ½ × base × height | ½ × 6 × 3 = 9 cm² |
| Circle | A = π r² | r = 2 cm → 4π ≈ 12.5664 cm² |
For a circle, r is the radius. If you have diameter d: first r = d ÷ 2, then π r². On vmbo (the more practical Dutch track) you practice the three formulas separately. On havo and vwo (middle and university-preparatory tracks) you combine them in a compound floor plan or in the base circle of a cylinder. Missing a right-triangle leg: Pythagorean theorem calculator.
| Conversion | Value | Watch |
|---|---|---|
| 1 m² in cm² | 10,000 cm² | 100 × 100, not 100 |
| 1 cm² in mm² | 100 mm² | 10 × 10 |
| Area vs volume | cm² vs cm³ | Plane ≠ solid |
Trapezium and parallelogram
A trapezium has two parallel sides a and b: A = ½ × (a + b) × height. A parallelogram has two pairs of parallel sides: A = base × height. Measure the height at a right angle to the base, not along the slanted side.
Trapezium with a = 8 cm, b = 4 cm and height 3 cm: 8 + 4 = 12; ½ × 12 × 3 = 18, so A = 18 cm².
Parallelogram with base 6 cm and height 4 cm: 6 × 4 = 24, so A = 24 cm².
Examples by level
A rectangle is 4 cm by 5 cm. What is the area?
- FormulaA = l × b
- Substitute4 × 5 = 20
- Unit20 cm² (not 20 cm)
Same length unit on both sides. The tool does not convert from m to cm.
Triangle with base 6 cm and height 3 cm, plus a circle with diameter 4 cm.
- Triangle½ × 6 × 3 = 9 cm²
- Radiusd ÷ 2: 4 ÷ 2 = 2 cm
- Circleπ · 2² = 4π ≈ 12.5664 cm²
Two separate areas; not volume. Diameter 4 cm is not the radius.
Right triangle with legs 6 cm and 8 cm: area and hypotenuse. Why is the hypotenuse not the height?
- Area½ × 6 × 8 = 24 cm² (perpendicular legs as base and height)
- Pythagoras6² + 8² = 36 + 64 = 100, c = 10 cm
- CheckA = ½bh uses the perpendicular height. The hypotenuse 10 cm is not a height.
If you only have slanted sides, find the height first with Pythagoras or a trig ratio.
Common mistakes
Wrong
Triangle as base × height, without the ½.
Right
A = ½ × base × height. The triangle is half of the enclosing rectangle.
Wrong
Putting the diameter into A = π r² as if it were the radius.
Right
First r = d ÷ 2. Diameter 4 cm is radius 2 cm, then π r².
Wrong
Answer in cm, or “converting” 1 m² to 100 cm².
Right
Area is length × length → cm². 1 m² = 100 × 100 = 10,000 cm².
Wrong
Mixing area and volume: writing cm² as cm³, or treating a floor as “volume”.
Right
Area = plane (cm²). Volume = solid (cm³). Solids: volume calculator or cylinder volume.
Practice
vmbo Rectangle 8 cm by 3 cm. What is A?
24 cm²
A = 8 × 3 = 24 cm².
vmbo Triangle, base 10 cm, height 4 cm. What is A?
20 cm²
A = ½ × 10 × 4 = 20 cm².
havo Circle with radius 5 cm. What is A? (4 decimal places)
78.5398 cm²
A = π · 5² = 25π ≈ 78.5398 cm².
havo Circle with diameter 10 cm. Same A as for r = 5?
Yes, 78.5398 cm²
r = 10 ÷ 2 = 5 cm, then the same π r².
vwo How many cm² is 1 m²? And is that volume?
10,000 cm²; no, not volume
1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm². Volume would be cm³.
vwo A right triangle has legs 6 cm and 8 cm. What is A, and what is the hypotenuse?
A = 24 cm², c = 10 cm
Area: ½ × 6 × 8 = 24. Hypotenuse: Pythagoras 6² + 8² = 36 + 64 = 100, c = 10. The hypotenuse is not a height.
In class
On vmbo, area is often a floor, a tile or a label: cm² on paper. On havo/vwo the same formula returns in compound figures and in the base circle of a cylinder: the cylinder volume calculator uses π r² as an intermediate step, then × h for volume. Cube, sphere and cone: volume calculator.
Rectangle, triangle and circle are in this one calculator: it is always the same question (how large is this flat shape?), with a different formula. Heron’s formula (three sides, no height) works differently; this calculator needs a base and a height.
Next step
- How does this work? The explanation and examples are further up this page.
Learning path
Frequently asked questions
How do you calculate the area of a rectangle?
A = l × b. Length and width in the same unit. 4 cm by 5 cm is 20 cm².
How do you calculate the area of a triangle?
A = ½ × base × height. Height is perpendicular to the base. ½ × 6 × 3 = 9 cm². A slanted side is not the height.
How do you calculate the area of a circle?
A = π r². With r = 2 cm, A = 4π ≈ 12.5664 cm². If you have the diameter: first r = d ÷ 2, then the same formula.
Why cm² and not cm?
You multiply two lengths. The product has unit length². 1 m² = 10,000 cm², not 100 cm².
Is area the same as volume?
No. Area is how large a flat shape is (cm²). Volume is how much fits inside (cm³). Cube, sphere and cone volume are on the volume calculator; the cylinder is on the cylinder volume calculator.
Related tools
Pythagorean theorem calculator
When you first need a missing side in a right triangle.
Volume calculator
Cube, sphere and cone in cm³ — not the same as area in cm².
Cylinder volume calculator
Volume: circle area π r² times the height.
Geometry
Hub for plane vs solid: area here, volumes on the sibling tools.