# perimeter

## Area of Rectangle = Length × Breadth: Conversations with a 9 year old

Children are taught many kinds of measures in the primary grades, like length, weight, volume, money, time and finally area and perimeter (which is nothing but measurement of length). While for teaching length, weight and volume, efforts are made to give students an exposure to informal/ non-standard units of measurement (and thus some implicit understanding of what we may use to measure something), the other measurement ideas start with the standard units, conversions and formulae.

## Fun with Dot Sheets

The ‘TearOut’ series is back, with perimeter and area. Pages 1 and 2 are a worksheet for students, while pages 3 and 4 give guidelines for the facilitator. This time we explore shapes with given perimeter or given area using the dots or the grid.

## π Enters the 5th Class

I write this to tell myself that it was not a dream...

This year I taught a bunch of fifth standard kids in Sahyadri School KFI (Krishnamurti Foundation India), who, like all others of their age, were high-energy kids; they were willing to explore but found it difficult to sit down in one place. I had a great relationship with them. The air in the classroom was of love, trust and wonder!

## A Minimum Perimeter Problem

LinkedIn reader Peter Lovasz asks: Among all triangles that share a given circle as incircle, which one has the smallest perimeter?

## Fagnano's Theorem - Alternative Proof

Fagnano’s Problem: In 1775, Giovanni Fagnano posed and solved the problem - “For a given acute angled triangle, determine the inscribed triangle of minimum perimeter.” Using calculus, Fagnano showed the solution to be the Orthic Triangle – a triangle formed by the feet of the three altitudes. A different proof was given in At Right Angles, Vol. 6, No.

## Area, Perimeter and Congruency

The topic of Perimeter and Area provides rich ground for teachers to examine the truth values of statements and then introduce the crucial ‘What-If ’ which can change a situation around completely.

## Inequalities in algebra and geometry 2

This article is the second in the ‘Inequalities’ series. We prove a very important inequality, the Arithmetic Mean-Geometric Mean inequality (‘AM-GM inequality’) which has a vast number of applications and generalizations. We prove it using algebra as well as geometry

## Teaching Area and Perimeter

Since they are introduced together, one frequently finds children mixing up the two concepts. Also formulae for arriving at these measures are brought in too quickly - well before the concepts are fully understood. One can avoid this problem by spacing out these two concepts. Area could be explored in the first stage as it occurs frequently in a child's everyday experiences.

## How to Prove It

In a previous issue of AtRiA (as part of the “Low Floor High Ceiling” series), questions had been posed and studied about polyominoes. In this article, we consider and prove two specific results concerning these objects, and make a few remarks about an open problem.

## Equalizers of a Triangle

In mathematics, breaking up is not hard to do!

## Pages

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