Derivation of the Area of a Rhombus

A rhombus is a parallelogram whose sides are congruent. The diagonals of rhombus are perpendicular to each other. They also bisect each other. In this post, we are going to find the general formula for finding the area of a rhombus using these properties. We are going to learn two methods.

Method 1

Consider the rhombus below.

area of a rhombus

We can divide it into two congruent triangles using diagonal d_1. Since the diagonals of a rhombus are perpendicular to each other, we can use d_1 as base and one half of d_2 as the height of the upper triangle (Why?). If we let A_T be the area of the upper triangle, then, calculating its area, we have  » Read more

Proof Without Words: If x >0, x + 1/x >=2

A picture is worth a thousand words, even in mathematics. Most of the time, complicated algebraic statements can be shown using geometric representations. One example is the sum of

\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots

which when added equals 1.

In this post, we show another geometric proof without words. Proof without words is not a proof per se but rather a representation that will help readers understand the proof.  » Read more

Prepare for Math Contests with MATHCOUNTS Trainer App

For math contest enthusiasts, if you are preparing for MATHCOUNTS or other middle school and high school math contests, then the MATHCOUNTS Trainer App is a good app that you can try. The app contains thousand of problems from previous School, Chapters, and National Mathcounts. Note that all problems in this app have full solutions. For those who are not familiar with MATHCOUNTS, it is a nationwide mathematics competitions for middle school students in the United States.

MATHCOUNTS Trainer App

In using this app, you can track your progress, compete with other players, and climb the Leaderboard.

The MATHCOUNTS Trainer app is FREE and available for iPhone, iPad, and iPod Touch. It also works offline.

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