Measuring Space: Perimeter and Area

Perimeter is the total length around the edge of a flat figure and is measured in units of length such as cm. Area is the amount of surface a figure covers and is measured in square units such as cm². Perimeter measures the boundary; area measures the space inside.

Heron's formula finds the area of a triangle when all three side lengths are known, without needing the height. First find the semi-perimeter s = (a + b + c)/2, then the area equals √(s(s−a)(s−b)(s−c)). It works for any type of triangle.

If the base and height are known, use Area = ½ × base × height. If only the three sides are known, use Heron's formula: find the semi-perimeter and apply √(s(s−a)(s−b)(s−c)). Both methods give the same area for the same triangle.

The area of a circle is πr² and the circumference (its perimeter) is 2πr, where r is the radius and π is about 22/7 or 3.14. The radius is the distance from the centre to the edge of the circle.

Break the composite figure into basic shapes such as rectangles, triangles, or circles. Find the area of each part using its formula, then add the areas together, or subtract when a region is cut out, to get the total area.

The semi-perimeter, half the sum of the sides, simplifies Heron's formula and makes the calculation symmetric in the three sides. Using s = (a + b + c)/2 keeps the expression √(s(s−a)(s−b)(s−c)) neat and easier to compute.