Solved Examples on Area of Equilateral triangle
Example 1: Find the area of the triangle whose all sides measure 4 units.
Solution:
As given all sides are of equal length hence, we can say that it is an equilateral triangle.
So we can apply the formula to directly find the area of this triangle.
Area = √3a2/4 = √3 × 42/4 = 4√3 units2
Example 2: Find the perimeter of the triangle whose sides are given as 3 cm, 4 cm, and 5 cm.
Solution:
Sum of all the sides of any triangle is the perimeter of triangle
Hence, the perimeter of this given triangle is (3 + 4 + 5) cm
i.e. Perimeter is 12 cm
Example 3: Find the height of the equilateral triangle whose side is 4 cm.
Solution:
The formula for the height is given by: h = √3a/2
h = (√3 × 4)/2 = 2√3 cm
Hence the height of the triangle is 2√3 cm
Example 4: Find the perimeter and area of the equilateral triangle whose side is given as 4 cm.
Solution:
Side (s) = 4 cm
For any equilateral triangle the perimeter is calculated as 3 × s
Primeter(P) = 3 × 4 = 12 cm
Area = √3a2/4
= √3(4)2/4
= √3(16) / 4 cm2
Area = 4√3 cm2
Example 5: Find the area of an equilateral triangle when the perimeter is 18 cm.
Solution:
Perimeter of an equilateral triangle = 18 cm
Perimeter of the equilateral triangle = 3a
3a = 18, a = 6
The length of side is 6 cm.
Area, A = √3 a2/ 4 sq units
= √3 (6)2/ 4 cm2 ⇒ 36 √3 / 4
= 9√3 cm2
Then area of the equilateral triangle is 9√3 cm2
Area of Equilateral Triangle
The area of an equilateral triangle is the amount of space enclosed within its three equal sides. For an equilateral triangle, where all three sides and all three internal angles are equal (each angle measuring 60 degrees), the area can be calculated using the formula [Tex]\frac{\sqrt{3}}{4}\times a^{2}[/Tex] where a is length of a side of Equilateral Triangle. An equilateral triangle is a triangle whose all side is equal to 60°.
In simple words, Area of an equilateral triangle is the space occupied by an equilateral triangle. Let’s know more about Area of Equilateral Triangle with formula, proof and examples.
Table of Content
- Area of Equilateral Triangle
- Area of Equilateral Triangle Formula
- Area of Equilateral Triangle Formula Proof
- Derivation of Area of Equilateral Triangle using Trigonometry
- Properties of Equilateral Triangle
- Solved Examples on Area of Equilateral triangle