Defining the Area of Equilateral Triangle
As a math student, you need to learn many topics, and equilateral triangles are among them. Get more information about their definition and basic properties to understand why they are so unique. Once you get this knowledge, your geometry assignments will be easier to complete, but if you still have any difficulties with your homework, the good news is that there are many qualified freelancers who can help you at quite reasonable rates. You only need to find their contact details online.
Before you start studying the area of equilateral triangle, find out more about this figure. Basically, it’s possible to split its definition into 2 key parts that mean sides and equivalent. This means that such triangles are figures with all equal sides and angles. You should know that the sum of all angles of any triangle is always 180 degrees so that every angle in equilateral triangles is 60 degrees.
Important Characteristics and Details
What about a perimeter of this type of triangle? Keep in mind that the perimeter of any figure is the sum of its side lengths. As you already know, all sides of equilateral triangles are equal so that you need only 1 side to end up with its perimeter. The main step that should be taken is just to add its length 3 times or multiply it by 3 (choose the easiest route).
If you need to find the area of equilateral triangle, don’t forget that this shape is quite special and different from other triangle types. If you remember that each side of such triangles is 60 degrees, and this is what makes them acute at the same time. That’s because acute triangles are the ones that have 3 angles less than ninety degrees. Besides, take into consideration a special case of isosceles triangles that have at least 2 equal sides and angles, and you’ll understand that equilateral triangles can be isosceles too.
Tips on How to Calculate the Area
One of the most widespread ways to find the area of any triangle is multiplying its height and base to divide this result by 2. However, there are many other methods that can be used to solve this problem, and your personal choice depends on specific dimensions that you have. To calculate the area of equilateral triangle, pay attention to other available formulas. If you have any questions, it’s worth asking them to professors before you start completing important geometry assignments. If you don’t have this opportunity, you can always count on the professional help offered by freelance authors online.
First, you can calculate the area of equilateral triangle by using their height and base. The latter one is the length of 1 side, which is commonly their bottom side, while their height is the length from the base to top corners, but make sure that it’s perpendicular to a given base. When dealing with right triangles, their height and base are 2 sides joined in a form of 90-degree angles. If you have non-right triangles, take into account that their height cuts across their middle. Once this goal is achieved, feel free to use a special formula to find the area of equilateral triangle, and this is where you need to plug in the lengths of both bases and heights. The next thing that should be done is solving this equation, but make sure that your answer is stated in square units because you’re dealing with a 2-dimensional space.
Second, it’s possible to use Heron’s formula or the length of every side. You should get started with calculating the semi-perimeter of a given triangle, and the main step that must be taken is adding up all sides before dividing this result by 2. Be sure to plug proper values into this formula to come up with the right area of equilateral triangle. It’s necessary to use the order of operations, and this means that you need to start with solving all that you can see inside the parenthesis. Subtract the values and multiply your result before you find a square root, and don’t forget to use square centimeters as your units.
Third, you can use 1 side of equilateral triangles to end up with their correct area. You need to find only 1 side because such shapes have equal sides and angles. It’s advisable to use the formula suitable for finding the area of equilateral triangle. The last step that should be taken is to plug the value of 1 side into your equation to solve it successfully.
Fourth, use the lengths of 2 sides and their included angle to achieve the same goal. Start with finding their right values, and take into consideration that an included angle is the one that is placed between 2 known sides of a given triangle. It’s required to find these values to find the right area of this shape by using this method. You need to write down a specific formula for finding it and plug exact values into it. Once these basic steps are taken, it’s quite easy to solve this equation, but ensure that your answer is stated in cubic units.
If you’re not 100% sure why a particular formula works that way, focus on a brief explanation. Imagine yourself making a copy of a given triangle and fitting them together. This is how you will end up with either a parallelogram or a rectangle. To find the area of equilateral triangle, you need to multiply their bases by heights, but since any triangle is their half, it’s necessary to solve for a half of base times height.
Guidelines on Drawing Equilateral Triangles
It’s another important skill that should be mastered by geometry students to achieve their academic success. Equilateral triangles come with equal sides and angles so that it can be a bit challenging to draw a perfect one manually. Be sure to use a proper circular object to succeed if your math homework includes this task. For instance, you can use a simple ruler to get all lines straight, and there are other effective tips that will come in handy.
Using a compass is a good idea to draw straight lines, but you need to lay a ruler on a piece of clean paper and trace your pencil along a straight edge. This is how you will come up with 1 side of your future equilateral triangle, and this means that you should draw 2 other lines with the same length. To find the right area of equilateral triangle, don’t forget that each angle is 60 degrees. Before you complete this task, ensure that you have enough room to draw each side.
The next step is spanning a segment by using your compass, so you should slide a pencil into it while making sure that that it’s quite sharp. The point of your compass should be put at 1 end of this segment while you set a pencil point at the other one. It’s also necessary to trace the quarter-circle arc without adjusting a compass point and changing its set width. You need to swing it in a quarter circle up and then away from a line segment.
Another thing that should be done is switching your compass around without altering its width, so move its point to the other end. You should draw the second arc by swinging a compass point to ensure that this arc will cross over the first one. For many students, this task is much easier than finding the area of equilateral triangle. Be sure to mark the point where both arcs cross because it’s the apex of your shape that must lie at the center of your line segment. Once this process is completed, you can draw 2 straight lines that lead to this point. Finish your triangle by using a ruler while drawing 2 line segments or its remaining sides. You also need to connect every end to the first line segment to points where arcs cross. Check whether they all are straight and erase arcs to end up only with a triangle to finish this job.
Besides, you can use any available object that has a circular base to do the same thing, which is quite convenient, even when calculating the area of equilateral triangle. If you don’t have any protractor or compass at hand, feel free to use this kind of object to trace out arcs. Remember that this simple method is just the same as using a compass, but you should be smart about it.
Start with picking a suitable circular object that can be any cylindrical object, such as a bottle. For instance, some geometry students decide to use a CD, while others have a circular tape roll. If you want to substitute its arc for the arc of your compass tracer, select the one with the right size. When using this original method, keep in mind that every side of your equilateral triangle must be as long as the radius of your circular object. Don’t forget about it when calculating the area of equilateral triangle. If you prefer to use a CD, try to imagine the shape that fits into its top-right quadrant.
Be sure to draw the first side and it must be straight and as long as the radius of your used object. When using a ruler, you can measure its diameter to draw a line which is half as long. If you don’t have this tool, place a circular object on the paper to trace its circumference with a pencil. Once you remove it, you will have a perfect circle.
If you don’t have a ruler, place the circular object on a piece of clean paper, then carefully trace a circumference with your pencil. Remove the object, and you will get a perfect circle. Use a straight edge to draw a line across its circle and you will get a point that is 100% equidistant from other points around its circumference. Finally, you need to trace one more arc by shifting a circular object to make its edge touch the end of a line segment to complete a triangle. Draw its remaining sides and make sure that they all are straight to complete this task.
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