Worksheet: Equilateral Triangles

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 (4π‘₯+7). Another side has length (3π‘₯+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 △𝐴𝐡𝐢.

Q5:

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

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

Q6:

In the figure below, 𝐴𝐡𝐢 is an equilateral triangle, 𝐷𝐡=𝐷𝐢, and π‘šβˆ π΅π·πΆ=112∘. Find π‘šβˆ π΄π΅π·.

Q7:

The area of an equilateral triangle is 256√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 1 ∢ 2
  • B 1 ∢ 1
  • C 1 ∢ 3
  • D 2 ∢ 1
  • E 3 ∢ 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 𝐴𝐡𝐢 is equilateral, and 𝐴𝐡=120cm, determine the lengths of 𝐴𝐢 and 𝐡𝐢.

  • A 60 cm, 60 cm
  • B 120 cm, 120 cm
  • C 120 cm, 240 cm
  • D 240 cm, 240 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 βˆ π‘Œ given π‘‹π‘Œπ‘ is a triangle where π‘‹π‘Œ=π‘Œπ‘=𝑍𝑋=6cm.

Q16:

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

Q17:

From a deck of cards that has a length of 72 inches, you take two cards and lean them together to create an equilateral triangle. What is the height of the triangle?

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

Q18:

In β–³π‘‹π‘Œπ‘, if π‘‹π‘Œ=π‘Œπ‘=𝑋𝑍, then π‘šβˆ π‘=.

Q19:

In β–³π‘‹π‘Œπ‘, if π‘‹π‘Œ=π‘Œπ‘=𝑋𝑍, then π‘šβˆ π‘Œ=.

Q20:

If the measure of the vertex angle of an isosceles triangle is 60∘, then the triangle is .

  • Aa right-angled triangle
  • Ba scalene triangle
  • Can equilateral triangle

Q21:

𝑋 π‘Œ 𝑍 is a triangle where π‘‹π‘Œ=π‘Œπ‘=𝑍𝑋=6cm. Find the value of βˆ π‘.

Q22:

In a triangle π‘‹π‘Œπ‘, if π‘‹π‘Œ=π‘Œπ‘=𝑋𝑍, what is π‘šβˆ π‘‹?

Q23:

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

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

Q24:

Find the area of the equilateral triangle whose circumcircle’s equation is π‘₯+π‘¦βˆ’16π‘₯+6𝑦+9=0.

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

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