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Class 9 Measuring Space: Perimeter and Area: cheat sheet
CBSE Mathematics. Find the area of any triangle from its three sides with Heron’s formula, and of a quadrilateral by splitting it into triangles.
Key ideas
- The perimeter is the sum of the sides; the semi-perimeter s is half of it.
- Heron’s formula needs only the three sides, no height.
- Check that the sides make a triangle: each side is less than the sum of the other two.
- For a quadrilateral, draw a diagonal to split it into two triangles and add their areas.
- Keep all sides in the same unit; the area comes out in square units.
Remember
| Semi-perimeter | s = (a + b + c)/2 |
| Heron’s formula | Area = √(s(s − a)(s − b)(s − c)) |
| Equilateral triangle, side a | Area = (√3/4)a² |
| Base and height | Area = ½ × base × height |
Watch out
- Using the full perimeter in place of s.
- Mixing units, such as metres and centimetres, in one calculation.
- Forgetting the square root, or writing the answer in m instead of m².
Worked example
A rhombus has sides of 20 cm and one diagonal of 24 cm. Find its area.
Working: the diagonal makes two triangles with sides 20, 20, 24, each 192 cm²
Answer: 384 cm²
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