Knowledge organisers

Area and Perimeter: CBSE Class 9 Maths knowledge organiser

Everything to know about area and perimeter on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Perimeter: The total length around the boundary of a shape.
Area: The amount of surface a flat shape covers, in square units.
Semi-perimeter: Half the perimeter, s = (a + b + c)/2, used in Heron's formula.

Key formulas

Arc; sector (angle \(\theta^\circ\))	\(l=\frac\theta{360}\cdot2\pi r,\) \(A=\frac\theta{360}\cdot\pi r^2\)
Heron, \(s=\frac{a+b+c}2\)	\(A=\sqrt{s(s-a)(s-b)(s-c)}\)
Inradius; equilateral triangle	\(A=rs;\) \(A=\frac{\sqrt3}4a^2\)
Brahmagupta (cyclic quad., \(s=\frac{a+b+c+d}2\))	\(A=\sqrt{(s-a)(s-b)(s-c)(s-d)}\)
Trapezium; rhombus	\(\tfrac12(a+b)h;\) \(\tfrac12d_1d_2\)

Worked example

Find the area of a triangle with sides \(13\), \(14\) and \(15\) cm.

\(s = 21\); area \(= \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{7056} = 84\) cm².

Common mistakes

Using the perimeter instead of the semi-perimeter \(s\) in Heron's formula.
Forgetting the two radii in the perimeter of a sector or the diameter in the perimeter of a semicircle.
Using Brahmagupta's formula for a quadrilateral that is not cyclic.
Mixing units (cm and m) or writing an area in cm instead of cm².

You should be able to…

Use Heron's formula, circle and arc formulas and the standard area formulas in one step.
Find missing sides from a perimeter, an inradius from Area = rs, and areas of rhombuses and isosceles triangles.
Find the area of a quadrilateral in two triangles and answer multi-part questions on tracks, sectors and signboards.
Use Brahmagupta's formula, altitudes from areas, and composite shapes with circles.

The printable sheet

Area and Perimeter knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Area and Perimeter knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers