Equilateral Triangle Practice Problems - Interactive Exercises

Master equilateral triangle concepts with step-by-step practice problems. Learn to calculate angles, perimeter, area, and identify properties of regular triangles.

📚Practice Equilateral Triangle Problems and Build Your Geometry Skills
  • Calculate angles in equilateral triangles knowing each measures exactly 60 degrees
  • Find perimeter by multiplying side length by 3 using the equal sides property
  • Determine unknown side lengths when given the perimeter of regular triangles
  • Solve complex area problems involving equilateral triangles and semicircles
  • Identify characteristics of regular three-sided polygons and their remarkable points
  • Apply Pythagorean theorem to find heights in equilateral triangle problems

Understanding Equilateral triangle

Complete explanation with examples

Definition of equilateral triangle

The equilateral triangle is a triangle that all its sides have the same length.

This also implies that all its angles are equal, that is, each angle measures 60° 60° degrees (remember that the sum of the angles of a triangle is 180° 180° degrees and, therefore, these 180° 180° degrees are divided equally by the three angles).

Detailed explanation

Practice Equilateral triangle

Test your knowledge with 20 quizzes

Is the triangle in the drawing an acute-angled triangle?

Examples with solutions for Equilateral triangle

Step-by-step solutions included
Exercise #1

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Answer:

Right triangle

Video Solution
Exercise #2

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer:

Obtuse Triangle

Video Solution
Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #5

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer:

Equilateral triangle

Video Solution

Frequently Asked Questions

What makes a triangle equilateral and how do I identify one?

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An equilateral triangle has all three sides of equal length and all three interior angles measuring exactly 60 degrees. It's also called a regular three-sided polygon because both sides and angles are equal.

How do I calculate the perimeter of an equilateral triangle?

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Since all sides are equal, multiply the length of one side by 3. For example, if one side is 5 cm, the perimeter is 3 × 5 = 15 cm.

What are the angle measures in an equilateral triangle?

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All three interior angles in an equilateral triangle measure 60 degrees each. Since triangle angles sum to 180°, each angle gets 180° ÷ 3 = 60°.

How do I find a missing side length if I know the perimeter?

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Divide the total perimeter by 3. For instance, if the perimeter is 33 cm, each side length is 33 ÷ 3 = 11 cm.

What special properties do equilateral triangles have?

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Key properties include: 1) All remarkable lines (heights, medians, bisectors) coincide, 2) All remarkable points meet at the same center point, 3) It's classified as an acute triangle since all angles are less than 90°.

How do I calculate the area of an equilateral triangle?

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Use the formula: Area = (side² × √3) ÷ 4. First find the height using the Pythagorean theorem, then apply the standard triangle area formula: (base × height) ÷ 2.

What's the difference between equilateral, isosceles, and scalene triangles?

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Equilateral triangles have all three sides equal, isosceles triangles have exactly two equal sides, and scalene triangles have no equal sides. This classification is based on side lengths.

Why is an equilateral triangle called a regular polygon?

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A regular polygon has all sides equal and all angles equal. Since equilateral triangles meet both criteria with three equal sides and three 60° angles, they qualify as regular three-sided polygons.

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