As the name suggests, ‘equi’ means Equal, an equilateral triangle is the one where all sides are equal and have an equal angle. The internal angles of the equilateral triangle are also the same, that is, 60 degrees. Here are the formulas for area, altitude, perimeter, and semi-perimeter of an equilateral triangle. Show
 Where, a is the side of an equilateral triangle. h is the altitude of an equilateral triangle. Equilateral Triangle Formulas\(\begin{array}{l}\large Area \;of \;an \;Equilateral \;Triangle = \frac{\sqrt{3}}{4}a^{2}\end{array} \) \(\begin{array}{l}\large Perimeter \;of \;an \;Equilateral \;Triangle = 3a\end{array} \) \(\begin{array}{l}\large Semi \;Perimeter \;of \;an \;Equilateral \;Triangle = \frac{3a}{2}\end{array} \) \(\begin{array}{l}\large Height \;of \;an \;Equilateral \;Triangle = \frac{\sqrt{3}}{2}a\end{array} \) Solved ExampleQuestion: Find the area, altitude, perimeter and semi-perimeter of an equilateral triangle whose side is 8 cm. Solution: Side of an equilateral triangle = a = 8 cm Area of an equilateral triangle = \(\begin{array}{l}\frac{\sqrt{3}}{4}\end{array} \) \(\begin{array}{l}a^{2}\end{array} \) = \(\begin{array}{l}\frac{\sqrt{3}}{4}\end{array} \) \(\begin{array}{l}\times\end{array} \) \(\begin{array}{l}8^{2}\end{array} \) cm2 = \(\begin{array}{l}\frac{\sqrt{3}}{4}\end{array} \) \(\begin{array}{l}\times\end{array} \) 64 cm2 = 21.712 cm2 Altitude of an equilateral triangle = \(\begin{array}{l}\frac{\sqrt{3}}{2}\end{array} \) a= \(\begin{array}{l}\frac{\sqrt{3}}{2}\end{array} \) \(\begin{array}{l}\times\end{array} \) 8 cm = 6.928 cm Perimeter of an equilateral triangle = 3a = 3 \(\begin{array}{l}\times\end{array} \) 8 cm = 24 cm Semi-Perimeter of an equilateral triangle = \(\begin{array}{l}\frac{3a}{2}\end{array} \) = \(\begin{array}{l}\frac{3\times 8}{2}\end{array} \) cm= \(\begin{array}{l}\frac{24}{2}\end{array} \) cm= 12 cm The side length of the triangle multiplied by #3#. The perimeter of any polygon is the sum of its side lengths. In an equilateral triangle, all of the sides are congruent (they are the same length). Thus, if an equilateral triangle has a side length of #2#, the perimeter is #2+2+2# because all of its sides are #2#. We can generalize this rule by saying that if an equilateral has side length #s#, its perimeter is #s+s+s#, which is equivalent to #3s#, or, the side length of the triangle multiplied by #3#. An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. The equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal. For instance, in the triangle, ABC are equal i.e. AB = BC = CA = a units. Also, ∠A, ∠B and, ∠C = 60° Properties of Equilateral Triangle
Perimeter of Equilateral Triangle Semi Perimeter of an Equilateral TriangleSemi Perimeter of an Equilateral Triangle = Let us assume a to be the side of an equilateral triangle. In other words, we have, Semi Perimeter of an Equilateral Triangle = Perimeter of an Equilateral Triangle when the area is givenLet us assume a to be the side of an equilateral triangle. Perimeter of an equilateral triangle can be computed using its area, which is given by, Now, We know, Perimeter of an equilateral triangle = Side + Side + Side Perimeter of an equilateral triangle, P is given by = 3 × a Therefore, the values a can be replaced by P/3. Perimeter of an Equilateral Triangle when Altitude is givenThe perimeter of an equilateral can be calculated when the altitude (height) of the triangle is given. We have, Height of an Equilateral Triangle = Upon substituting the values of the perimeter of the equilateral triangle, we have, Perimeter of an equilateral triangle = Side + Side + Side Perimeter of an equilateral triangle = 3 × a Therefore, Height (or Altitude ) = Sample QuestionsQuestion 1. Calculate the perimeter of an equilateral triangle if the side of the triangle is 30√3 cm. Solution:
Question 2. If the side of an equilateral triangle is 90 m, then find the perimeter and semi-perimeter of the triangle? Solution:
Question 3. Consider that the area of an equilateral triangle is 100√3 cm2, Then calculate its perimeter? Solution:
Question 4. Find the perimeter of an Equilateral triangle if the height of the triangle is 35√3 m. Solution:
Question 5. If the side of an equilateral triangle is 23 cm, then find the perimeter and height of the equilateral triangle? Solution:
How do you get the perimeter of an equilateral triangle?The basic formula that is used to calculate the perimeter of an equilateral triangle is: P = 3a, where 'a' represents one side of the triangle. Since all the three sides of an equilateral triangle are equal, the sum becomes a + a + a = 3a.
How do you find the perimeter of a triangles?The formula for the perimeter of a triangle is the sum of the length of all the sides of a triangle. For example, if the side lengths of a triangle are 3 cm, 4 cm, and 5 cm, then the perimeter of the triangle will be 3 + 4 + 5 = 12 cm.
What is a formula of equilateral triangle?An equilateral triangle is the one in which all three sides are equal. It is a special case of the isosceles triangle where the third side is also equal. In an equilateral triangle ABC, AB = BC = CA.
What does the perimeter of an equilateral triangle equal?Because the sides of the equilateral triangle are equal, the perimeter is equal to 3a.
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How do you find the perimeter of an equilateral triangle
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