An equilateral triangle is a triangle whose three sides all have the same length. Its three angles are also equal, so each one measures 60 degrees. With side length a, its perimeter is 3a and its area is √34a2. Every equilateral triangle is also isosceles and acute.
Equal sides force equal angles. Because the three angles share 180°, each one is 60°.
Formal definition and notation
Triangle ABC is equilateral if AB = BC = CA. Equivalently, it is equiangular: m∠ A = m∠ B = m∠ C = 60°. For sidea, the height is h = √32a and the area is A = √34a2. It is the regular polygon with three sides.
Symbol
Read it as
Meaning
tick marks
congruent marks
one matching tick on each side shows all three sides are equal
△ ABC
triangle A B C
the triangle with vertices A, B and C
Key facts
Each angle is 180° ÷ 3 = 60°, whatever the side length.
An equilateral triangle has 3 lines of symmetry, each from a vertex to the midpoint of the opposite side.
Every equilateral triangle is isosceles (it has at least two equal sides), but most isosceles triangles are not equilateral.
An isosceles triangle needs only two equal sides, such as 7, 7, 4. Equilateral needs all three equal. Every equilateral triangle counts as isosceles, not the other way round.
Equilateral Trianglevs.Equiangular
Equiangular means all angles are equal. For triangles the two words describe the same shapes; for other polygons they differ (a rectangle is equiangular but usually not equilateral).
Quick check: 3 questions
Question 1 of 3
What is each angle of an equilateral triangle with sides of 9 inches?
Show answer and explanation
Answer: D. All three angles are equal and add to 180°, so each is 60°, regardless of side length. 9° mixes up sides and angles, 90° is a right angle, and 45° belongs to an isosceles right triangle.
Question 2 of 3
An equilateral triangle has side 8 cm. What is its area?
Show answer and explanation
Answer: B.√34 × 64 = 16√3 ≈ 27.7. 32 uses the side as the height, 64 is a square’s area, and 4√3 is the height.
Question 3 of 3
Which statement is always true?
Show answer and explanation
Answer: C. Isosceles means at least two equal sides, and an equilateral triangle has three. The reverse fails (5, 5, 8), its angles are all 60°, so none is right, and it has 3 lines of symmetry.
Equilateral Triangle: frequently asked questions
Is an equilateral triangle also isosceles?
Yes, under the usual definition. An isosceles triangle has at least two equal sides, and an equilateral triangle has three, so it qualifies. This is like a square being a special rectangle. Some older books define isosceles as exactly two equal sides; if a problem says so, follow its definition.
How do you find the area of an equilateral triangle?
Use A = √34a2, where a is the side. For side 4: √34 × 16 = 4√3 ≈ 6.93. This comes from 12 × base × height with height √32a, found by the Pythagorean theorem on half the triangle. Leave the answer as 4√3 for an exact value, or round the decimal at the end.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 5.G.B.3, CCSS 5.G.B.4, CCSS HSG-CO.C.10
Cite this entry
Effortless Math Team. “Equilateral Triangle.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/equilateral-triangle/
Flashcard
TermEquilateral Trianglethree equal sides
DefinitionA triangle with all sides equal and all angles 60°. Area √34a2: side 2 gives √3.
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