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.

  • Aπ‘₯=20, 𝑦=29
  • Bπ‘₯=20, 𝑦=23
  • Cπ‘₯=20, 𝑦=23
  • Dπ‘₯=32, 𝑦=29
  • Eπ‘₯=32, 𝑦=23

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?

  • A1∢2
  • B1∢1
  • C1∢3
  • D2∢1
  • E3∢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.

  • A60 cm, 60 cm
  • B120 cm, 120 cm
  • C120 cm, 240 cm
  • D240 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?

  • A7√32 inches
  • B7√36 inches
  • C74 inches
  • D7√34 inches
  • E7√22 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:

π‘‹π‘Œπ‘ 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.

  • A𝑃=3𝑏
  • B𝑃=π‘οŠ¨
  • C𝑃=π‘οŠ©
  • D𝑃=𝑏+2
  • E𝑃=𝑏+3

Q24:

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

  • A48√3 square units
  • B6√3 square units
  • C12√3 square units
  • D96√3 square units

Q25:

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

  • A1∢3
  • B3∢1
  • C1∢4
  • D4∢1

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