Area and Perimeter Formulas – 2D Shapes Cheat Sheet

A six-page formula reference covers area and perimeter (or circumference) formulas for twelve 2D shapes, each with a labeled diagram, in matching colour and black-and-white versions.

Grades: Grades 5–12
File type: PDF
Preparation: Print ready

Updated May 22, 2023

Subject: Geometry, Math
Topic: Perimeter Formulas, Area Formulas
Resource types: Graphic Organizers, Teacher Tools
Preparation: Print ready

From the author

About this resource

Perimeter and Area Formulas of 2D Shapes | Cheat Sheet

This valuable resource is designed to make learning mathematics easier for students. Specializing in Geometry, this cheat sheet presents a wide range of formulas dedicated to calculating the perimeter and area of various two-dimensional shapes, accommodating students from grades 5 all the way through to 12.

Uses:

It can be incorporated into group discussions for dissecting each formula in detail.
Students can be divided into small groups to explore specific shapes separately using this sheet.
It acts as a useful homework tool easily referred during practice by pupils at home.

The sheet includes Perimeter and Area formulas for common two-dimensional shapes like: Square, Rectangle, Parallelogram,Triangle,Trapezoid,Circle,Sector of Circle,Ellipse,Pentagon up till Octagon including regular polygons. It features an accompanying image for each shape that aids in easy identification based on their unique dimensions aiding not just calculations but also enhances visual understanding.

Bonuses:

Saves time compared to searching through textbooks or notes when under exam pressure or seeking immediate clarity while practicing problems–this guide offers immense reference benefits promptly.
The accuracy in calculations is enhanced with appropriate application of relevant variables per particular formula; thus diminishing potential errors root cause boosting academic performance levels substantially.

The digital product comes as PDF files containing three pages filled with coloured formulas and three more pages featuring black-and-white versions which are ideal for printing. It allows easy adaptability due to user preferences or resources available thereby granting every student unrestricted access irrespective wherever they are studying: be it during classroom sessions or at home reviewing.

Proximity to better comprehension and precision - this brilliant academic tool reinforces crucial foundational knowledge, driving students towards greater mathematical confidence.

In the classroom

Teaching tips & learning objectives

Learning objectives

Locate the correct area formula for a given 2D shape using the labeled variable key.
Locate the correct perimeter or circumference formula for a given 2D shape using the labeled variable key.
Identify which variables (side length, radius, height, base, angle) a given shape's formulas require.

Teaching tips

Use this as a quick-reference handout during geometry units rather than as a standalone lesson, since it contains no practice problems.
Print the black-and-white pages (4-6) for students who need an inexpensive personal copy to keep in a binder, and reserve the colour pages (1-3) for a classroom wall reference.
Pair this sheet with a separate practice worksheet, since students will need worked examples in addition to the formulas themselves to build fluency.

Skills covered

Formula lookup and application — students locate and apply the correct area or perimeter formula for a named 2D shape from a reference sheet rather than deriving it.
Variable identification — each shape's diagram labels its specific variables (e.g., base and height for a triangle, semi-major and semi-minor axis for an ellipse), so students learn to match a shape's dimensions to formula notation.
Coverage from basic to advanced shapes — the same reference spans elementary-level shapes (square, rectangle, triangle) through more advanced ones (sector of a circle, ellipse, regular polygon) with the angle-based formulas those require.

Good to know

Questions teachers ask about this resource

Does this sheet include example problems showing the formulas in use, or only the formulas themselves?

Only the formulas and labeled diagrams themselves — no worked example calculations or practice problems are included on any of the six pages, so it functions as a lookup reference rather than a practice worksheet.

Do the colour and black-and-white versions differ in content?

No — the same twelve shapes and formulas appear twice: pages 1 through 3 in colour, and pages 4 through 6 as a black-and-white duplicate intended for economical printing.