Area

Interesting problem on area and triangle.

The article talks about a simple activity which can be performed with students of primary, middle and high school. The shape that is used to discuss here is a square and hence it is expected that students know the basic properties of a square. The article also talks about using lines. Even if students don't have a Euclidean notion of definition of a line, that idea can be instilled as the teacher executes this activity.

On the Facebook page (AtRiUM: At Right Angles, Us and Math) linked to this magazine, one of our contributors, Arsalan Wares, has been astonishingly prolific in posting problems. A good many of these have had to do with regular hexagons; more specifically, with the areas of polygonal regions drawn within such hexagons. It is both astonishing and pleasing to see such a rich diversity of problems arising from this simple and familiar structure.

Websites and focus interest groups are a good source for interesting problems. But it’s rarely that one gets down to solving these; more often they go into a to-do list. We hope that the solution presented here will encourage you to try more of these. Look at the steps of the process: Visualization, definition of the problem, connection to known formulas and then good old mathematical processing. Problem solved!

In this article, we study the following problem. Three circles of equal radius r are centred at the vertices of an equilateral triangle ABC with side 2a. Here we assume that r > a. Find the area of the three-sided region DEF enclosed by all three circles, in terms of r and a.

Consider a solid sphere of radius r. Suppose it is melted and the molten mass is recast into two solid spheres of radii r 1 and r 2 . Does the total surface area increase, decrease or remain the same, if it is assumed that there is no loss of matter in the whole process?

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.

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

Find the solution to the circle area problem posed in the earlier issue of AtRiA.

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.

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