## The Basics of Direct Proportion

A car travels at 40 kilometers per hour traveled for 7 hours. The table of the distances traveled with respect to time is shown below.

Observe the relationship between the distance traveled and the time. As the time increases, the distance traveled increases. If the number of hours increases two times, then the distance also increases two times. Between hour 1 and hour 2, the increase in time is 1 hour, and the increase in distance is 40 kilometers. Between hour 3 and hour 5, the increase in time is 2 hours, and the increase in distance is 2(40) = 80 kilometers.

If there are two changing quantities $x$ and $y$ and if the value of $x$ changes 2 times, 3 times, and so on, $y$ also changes 2 times, 3 times, and so on respectively, we can say that $y$ is directly proportional to $x$. In the relationship above, distance is directly proportional to time.

## Math and Multimedia turns 6

Math and Multimedia turns 6 today. This blog started in 2009 in WordPress.com and since then has been updated at least three times a week. Mathematics and Multimedia is a blog that discusses mathematics concepts from elementary school mathematics up to university mathematics, provides suggestions and tutorials on how to use multimedia materials and apps in mathematics, and share useful teaching and learning materials.

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## 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.

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