Worksheet: Equilateral Triangles

Practice

In this worksheet, we will practice identifying equilateral triangles by their equal side lengths or equal angle measures to find a missing side length, perimeter, or area.

Q1:

Find the perimeter of the shape below.

Q2:

One side of an equaliteral triangle has length ( 4 π‘₯ + 7 ) . Another side has length ( 3 π‘₯ + 8 ) . Find the perimeter of the triangle.

Q3:

The perimeter of an equilateral triangle is equal to the perimeter of a rectangle with a length of 5 cm and a width of 4 cm. Find the length of one side of the triangle.

Q4:

Find the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q5:

In the figure, find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 2 0 , 𝑦 = 2 9
  • B π‘₯ = 3 2 , 𝑦 = 2 9
  • C π‘₯ = 3 2 , 𝑦 = 2 3
  • D π‘₯ = 2 0 , 𝑦 = 2 3
  • E π‘₯ = 2 0 , 𝑦 = 2 3

Q6:

In the figure below, 𝐴 𝐡 𝐢 is an equilateral triangle, 𝐷 𝐡 = 𝐷 𝐢 , and π‘š ∠ 𝐡 𝐷 𝐢 = 1 1 2 ∘ . Find π‘š ∠ 𝐴 𝐡 𝐷 .

Q7:

The area of an equilateral triangle is 2 5 6 √ 3 cm2. Find the side length.

Q8:

The diagram shows an equilateral triangle. Find the length of its sides.

Q9:

What is the ratio of the length of a side of an equilateral triangle to its perimeter?

  • A 3 ∢ 1
  • B 1 ∢ 1
  • C 1 ∢ 2
  • D 1 ∢ 3
  • E 2 ∢ 1

Q10:

A triangle has three sides equal in length and a perimeter of 24 length units. Find the length of one of its sides.

Q11:

Calculate the length of one of the sides of an equilateral triangle which has a perimeter of 93 m.

Q12:

Given that triangle 𝐴 𝐡 𝐢 is equilateral, and 𝐴 𝐡 = 1 2 0 c m , determine the lengths of 𝐴 𝐢 and 𝐡 𝐢 .

  • A 60 cm, 60 cm
  • B 240 cm, 240 cm
  • C 120 cm, 240 cm
  • D 120 cm, 120 cm

Q13:

If one of the sides of an equilateral triangle measures 50 cm, calculate its perimeter.

Q14:

If a square with side length 54 cm has the same perimeter as an equilateral triangle, what is the side length of the triangle?

Q15:

Find the value of ∠ π‘Œ given 𝑋 π‘Œ 𝑍 is a triangle where 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑍 𝑋 = 6 c m .

Q16:

What is the measure of each angle in an equilateral triangle?

Q17:

From a deck of cards that has a length of 7 2 inches, you take two cards and lean them together to create an equilateral triangle. What is the height of the triangle?

  • A 7 √ 3 6 inches
  • B 7 4 inches
  • C 7 √ 3 2 inches
  • D 7 √ 3 4 inches
  • E 7 √ 2 2 inches

Q18:

In β–³ 𝑋 π‘Œ 𝑍 , if 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑋 𝑍 , then π‘š ∠ 𝑍 = .

Q19:

In β–³ 𝑋 π‘Œ 𝑍 , if 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑋 𝑍 , then π‘š ∠ π‘Œ = .

Q20:

If the measure of the vertex angle of an isosceles triangle is 6 0 ∘ , then the triangle is .

  • A a right-angled triangle
  • B a scalene triangle
  • C an equilateral triangle

Q21:

𝑋 π‘Œ 𝑍 is a triangle where 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑍 𝑋 = 6 c m . Find the value of ∠ 𝑍 .

Q22:

In a triangle 𝑋 π‘Œ 𝑍 , if 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑋 𝑍 , what is π‘š ∠ 𝑋 ?

Q23:

Write an equation for the perimeter, 𝑃 cm, of an equilateral triangle with sides of length 𝑏 cm.

  • A 𝑃 = 𝑏 + 3
  • B 𝑃 = 𝑏 3
  • C 𝑃 = 𝑏 2
  • D 𝑃 = 3 𝑏
  • E 𝑃 = 𝑏 + 2

Q24:

Find the area of the equilateral triangle whose circumcircle’s equation is π‘₯ + 𝑦 βˆ’ 1 6 π‘₯ + 6 𝑦 + 9 = 0   .

  • A 9 6 √ 3 square units
  • B 6 √ 3 square units
  • C 1 2 √ 3 square units
  • D 4 8 √ 3 square units

Q25:

Write this ratio in its simplest form: The ratio of the side length of an equilateral triangle to its perimeter.

  • A 1 ∢ 4
  • B 3 ∢ 1
  • C 4 ∢ 1
  • D 1 ∢ 3

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