How To Solve An Area Of A Triangle

September 6, 2019

In mathematics, every complex principle was developed from simple concepts with less complexity. Realizing this changed my general understanding of mathematical problems and how to solve them effectively. This simple understanding also affected the way I saw an area of a triangle, the general formula and how it is solved. 

This simple understanding that changes my view of maths as a whole is what am willing to share right here for maths students finding it difficult to solve an area of a triangle or master the use of its formula. I strongly believe this will make impacts in so many students out there just the way it did with me. 

But before I begin to share all have been able to acquire about an area of a triangle, let’s take a quick look at how an area of triangle came to be. 

What is an area of a triangle? 

The first thing I was able to understand about triangles is that they aren’t just random shapes. They are shapes extracted from a parallelogram when divided. By dividing a parallelogram along its axis, we will be left with two separate triangles of equal shapes and sizes. From this division process, the formula for calculating the area of a triangle was derived. 

To further explain this, the area of a parallelogram is A = B * H. If the division process is applied, the formula of a parallelogram is divided by two, leaving us with the formula for calculating the area of a triangle which all know now ( A= 1/2 B*H) B and H here represents the base and height of a triangle respectively. 

The Base which is represented by B is the side of the triangle. While the height is the line perpendicular to the base of a triangle. (Note: both the base and the height has to be perpendicular to each other before they can be considered as authentic base and height lines) Although the height is usually not always the same in all triangles. They often take different positions depending on the type of triangle. 

For right-angle triangles, the height is always perpendicular to the base of the triangle. While in symmetry triangles, the lateral sides are not perpendicular to the base. To find the height of the triangle, a dotted line is traced inside the triangle to help find the height. 

How to calculate the area of a triangle 

Just like every other elementary maths problem, all that is needed is a formula. And since we now have a better understanding of what this formula is all about, all we need to do is make use of it the right way.

Let us take a look at an example to help explain this formula better and how it is being used.  Let’s say we are asked to find the area of an acute triangle, given the base as 15 inches and the height as 4 inches. To solve this, all we need to do is introduce our general formula which is A=1/2 B*H. By introducing the values for B and H and simplifying the equation( A=1/2 15*4), the area will be equals to 30 inches square. 

By now you should know that solving an area of a triangle is a big part of the math sections of the SHSAT. You can prepare for the SHSAT at Caddell Prep if you need further assistance.