Area & Perimeter Calculator – Tutorial

Geometry: Area and Perimeter — Detailed Guide for Students

On this page you will clearly learn the concepts of "area" and "perimeter." The calculator includes 3 shapes: Circle, Rectangle, and Triangle (base + height).

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1) The Difference Between Area and Perimeter

1.1 What is perimeter?

Perimeter is the total distance around the boundary of a shape. Think of it as the sum of all the sides.

• Unit: length units like cm, m, km.
• E.g.: Perimeter of a rectangle = sum of all sides.

1.2 What is area?

Area is the size of the surface a shape covers. Think of it as "how many unit squares fit inside?"

• Unit: squared units like cm², m².
• E.g.: A 3 m × 2 m rug has an area of 6 m².

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2) Circle

2.1 Key measurement: Radius (r)

The most important value in a circle is the radius r. It is the distance from the center to the edge.

2.2 Circle area formula

Area = π · r²

• r² means: r × r
• π (pi) ≈ 3.14159... (often approximated as 3.14)

2.3 Circle perimeter (circumference) formula

Perimeter = 2 · π · r

2.4 Quick example

• r = 5
• Area = π · 25 ≈ 78.54
• Perimeter = 2 · π · 5 ≈ 31.42

Note: The calculator uses the exact value of π (Math.PI) for more precise results.

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3) Rectangle

3.1 Rectangle measurements

A rectangle has two measurements: width (w) and height (h).

3.2 Rectangle area formula

Area = w · h

Think of it like "rows × columns." For example, a 10 cm × 6 cm rectangle has an area of 60 cm².

3.3 Rectangle perimeter formula

Perimeter = 2 · (w + h)

• Opposite sides are equal: w + w + h + h = 2(w + h)

3.4 Quick example

• w = 10, h = 6
• Area = 10 · 6 = 60
• Perimeter = 2 · (10 + 6) = 32

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4) Triangle (Base + Height) — Why is perimeter not shown?

4.1 Triangle area formula

Area = (Base · Height) / 2

The "height" here is the perpendicular distance from the base (90° angle). The height is not necessarily the same as any side of the triangle.

4.2 Why divide by 2?

Imagine a rectangle with the same base and height. If you cut it diagonally, you get two equal triangles. So the triangle area is half that of the rectangle with the same base and height.

4.3 Why is perimeter not calculated?

The perimeter of a triangle requires all 3 sides:

Perimeter = a + b + c

But this calculator only has base and height. Different triangles can have the same base and height but different side lengths → different perimeters. So only the area is safely provided.

4.4 Quick example

• Base = 8, height = 5
• Area = (8 · 5) / 2 = 20

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5) Errors and Common Mistakes

• Negative values: r, w, h, base, and height must all be greater than 0.
• Unit confusion: perimeter uses length units; area uses squared units.
• Triangle height: the height must always be perpendicular to the base.

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6) How to Use This Calculator

1. Select a shape: Circle / Rectangle / Triangle
2. Enter the required measurements
3. Click Calculate

Tip: Some fields (like w/h) depend on the selected shape — just fill in the relevant ones.