Area of equilateral triangle

Area of a triangle is the region enclosed by it, in a two-dimensional plane. As we know, a triangle is a closed shape that has three sides and three vertices. Thus, the area of a triangle is the total space occupied within the three sides of a triangle. The general formula to find the area of the triangle is given by half of the product of its base and height. In general, the term “area” is defined as the region occupied inside the boundary of a flat object or figure. The measurement is done in square units with the standard unit being square meters (m 2). For the computation of area, there are predefined formulas for squares, rectangles, circles, triangles, etc. In this article, we will learn the area of triangle formulas for different types of triangles, along with some example problems. What is the Area of a Triangle? The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it . It is applicable to all types of triangles , whether it is scalene, isosceles or equilateral. To be noted, the base and height of the triangle are perpendicular to each other. The unit of area is measured in square units (m 2 , cm 2 ). Example: What is the area of a triangle with base b = 3 cm and height h = 4 cm? Using the formula, Area of a Triangle, A = 1/2Â...

When you know all three sides of a triangle, you can find the area using where s is the length of any side of the triangle. Note that Methods for finding triangle area If you know: Use: Base and altitude All 3 sides Two sides and included angle x,y coordinates of the vertices or The triangle is equilateral

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Area Of Equilateral Triangle The area of an equilateral triangle is the amount of space that it occupies in a 2-dimensional plane. To recall, an equilateral triangle is a Area of an Equilateral Triangle Formula The formula for the area of an equilateral triangle is given as: Area of Equilateral Triangle (A) = (√3/4)a 2 Where a = length of sides Learn more about Derivation for Area of Equilateral Triangle There are three methods to derive the formula for the area of equilateral triangles. They are: • Using basic triangle formula • Using rectangle construction • Using trigonometry Deriving Area of Equilateral Triangle Using Basic Triangle Formula Take an equilateral triangle of the side “a” units. Then draw a perpendicular bisector to the base of height “h”. Deriving Area Of Equilateral Triangle Now, Area of Triangle = ½ × base × height Here, base = a, and height = h Now, apply a 2 = h 2 + (a/2) 2 ⇒ h 2 = a 2 – (a 2/4) ⇒ h 2 = (3a 2)/4 Or, h = ½(√3a) Now, put the value of “h” in the area of the triangle equation. Area of Triangle = ½ × base × height ⇒ A = ½ × a × ½(√3a) Or, Area of Equilateral Triangle = ¼(√3a 2) Deriving Area of Equilateral Triangle Using Rectangle Construction Consider an equilateral triangle having sides equal to “a”. How to find Area of Equilateral Triangle? Here, the length of the equilateral triangle is considered to be ‘a’ and the height as ‘h’ So the area of an equilateral triangle = Area of a rectangle = ½×a×h …………....

• • • • • • What Is the Area of an Equilateral Triangle? Area of an equilateral is the region bounded within the three sides of the triangle. In other words, the area of an equilateral triangle is the total region enclosed within the boundary of the triangle. It is calculated using the simple formula $\frac \times a^2$, where “a” is the length of the side. An equilateral triangle is a triangle in which all sides are equal and all interior angles are congruent. Each angle of an equilateral triangle measures $60^\circ$. In the equilateral triangle ABC shown below, the area of the triangle is the green shaded region. Area of an Equilateral Triangle Formula The formula for area of equilateral triangle is given by: $Area = \frac\times(a)^2$ How to Find the Area of an Equilateral Triangle To find the area of an equilateral triangle, simply substitute the length of the side in the following formula: $Area = $\frac$ square units Practice Problems on Area of Equilateral Triangle The area of an equilateral triangle is the region enclosed within the boundary of the triangle. We can calculate the area of triangle using the formula $\frac$ , where a is the side of the triangle. It is measured in square units. The perimeter of an equilateral triangle is the length of the outline of the equilateral triangle. We can calculate the perimeter of equilateral triangle by using the formula 3a where a is the side of the triangle.

First draw the height - due to the symmetry of equilateral triangles, it will start at the midpoint of whichever side you choose to start from, and end at the opposite vertex (point/corner). In effect you will split the equilateral triangle into two congruent right triangles. Now consider one of these two right triangles by itself. If the equilateral triangle has sides of length x, then the hypotenuse of our right triangle will also be x. We also know that the side opposite the 30 degree angle has length x/2, since we split that side of the triangle in half to construct this right triangle. Since you know two of the sides of a right triangle, you can use the Pythagorean theorem to find the length of the 3rd. (x/2)^2 + m^2 = x^2 x^2/4 + m^2 = x^2 m^2 = (3*x^2)/4 m = (x*sqrt(3))/2 Where m is the height of the right triangle, which is equal to the height of the equilateral triangle. Incidentally, this derivation also proves the shortcut for the ratio of the sides in a 30-60-90 triangle, since the effect of cutting an equilateral triangle in half is to create 2 30-60-90 triangles. We don't know what the height is without working it out. Pythagoras' theorem says that in a right triangle, the area of a square drawn on the longest side (the hypotenuse) is equal in area to the areas of the two squares drawn on the other two sides (the legs), added together. The square on the side with length s/2 is 1/4 of the area of the square on the side with length s, so a square on the height ...