How do you calculate square meters?

For a rectangle, multiply length × width (both in meters). A room of 5 m × 4 m has an area of 20 m². For irregular shapes, divide them into simple forms (rectangles, triangles) and add the partial areas.

How do you calculate circle area?

Circle area = π × r² (Pi times radius squared). If you only know the diameter, halve it first: r = d / 2. Example: A circle with radius 3 m has area π × 3² = 28.27 m².

What is the difference between area and perimeter?

Area measures the content of a flat shape (e.g. in m²) — how much space it covers. Perimeter is the length of the outer boundary (in m). For a 3 × 4 m rectangle, the area is 12 m² and the perimeter is 14 m.

How do you convert m² to cm²?

1 m² = 10,000 cm² (because 1 m = 100 cm, so 100 × 100 = 10,000). Multiply the area in m² by 10,000. Conversely: cm² divided by 10,000 gives m². Similarly: 1 m² = 1,000,000 mm².

How do you calculate triangle area?

Triangle area = (base × height) / 2. The height is perpendicular to the base. Example: base 6 m, height 4 m → area = (6 × 4) / 2 = 12 m². Alternatively: use Heron's formula when all three sides are known.

One hectare (ha) = 10,000 m² = 100 m × 100 m. It is mainly used in agriculture and forestry. For comparison: a football field is about 0.714 ha (7,140 m²). 1 km² = 100 ha.

How do you calculate living space?

Per the German WoFlV regulation: rooms with ceiling height above 2 m count 100%. Areas with 1–2 m height (e.g. under sloped ceilings) count 50%. Below 1 m does not count. Balconies and terraces are typically counted at 25%.

How do you calculate trapezoid area?

Trapezoid area = ((a + b) / 2) × h, where a and b are the two parallel sides and h is the height (perpendicular distance). Example: a = 4 m, b = 8 m, h = 5 m → area = ((4 + 8) / 2) × 5 = 30 m².

π (Pi) is the ratio of a circle's circumference to its diameter — a mathematical constant with the value ≈ 3.14159. Pi is irrational (infinitely many non-repeating decimals) and appears in formulas for circle area (πr²), circumference (2πr) and ellipse area (πab).

How do you calculate irregular shapes?

Calculate irregular areas by decomposing them into simple partial shapes (rectangles, triangles, circle segments) and summing them up. For plots, the Shoelace formula (Gauss area formula) helps: enter the vertex coordinates and get the exact area. Modern GPS apps calculate the area automatically when walking the property boundaries.

Triangle Area: 4 Methods Compared | Area Calculator

Four Methods for Calculating Triangle Area

There are several ways to calculate the area of a triangle. The right method depends on which measurements are known.

Method 1: Base Times Height

The standard formula A = (Base x Height) / 2 is the simplest and most commonly used. The height must be perpendicular to the chosen base. In a right triangle, the two legs directly serve as base and height.

Example: Triangle with base 8 m and height 5 m. Area = (8 x 5) / 2 = 20 m2.

Important: Any of the three sides can serve as the base. The corresponding height is the shortest distance from the opposite vertex to the (extended) base line.

Method 2: Heron's Formula

When all three side lengths are known but no height, use Heron's formula. First calculate the semi-perimeter: s = (a + b + c) / 2. Then: A = sqrt(s x (s-a) x (s-b) x (s-c)).

Example: Triangle with sides a = 5 m, b = 6 m, c = 7 m. s = (5+6+7)/2 = 9. A = sqrt(9 x 4 x 3 x 2) = sqrt(216) = 14.70 m2.

Method 3: Cross Product (Coordinates)

When vertex coordinates are known, calculate the area with: A = |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| / 2. This method is especially useful in surveying and computer graphics.

Method 4: Trigonometry

When two sides and the included angle are known: A = (a x b x sin(gamma)) / 2. This method is frequently used in geodesy and navigation.

Example: Two sides a = 10 m and b = 8 m with included angle 30 degrees. A = (10 x 8 x sin(30)) / 2 = (10 x 8 x 0.5) / 2 = 20 m2.

Which Method When?

Method 1 (Base x Height) is ideal when a side and its corresponding height can be directly measured (e.g., construction and renovation). Method 2 (Heron) is suitable when only the three sides are known (e.g., land surveying). Method 3 (Coordinates) is used with digital maps and CAD. Method 4 (Trigonometry) is applied when an angle is known.

Special Cases

Equilateral triangle: A = (sqrt(3) / 4) x a2 (with side length a). Isosceles triangle: The height bisects the base into two equal halves. Right triangle: The area is simply (leg1 x leg2) / 2.