Worksheet: Applications of Similar Polygons

In this worksheet, we will practice using the properties of similar polygons to solve algebraic expressions and equations.

Q1:

If 𝐴𝐵𝐶𝐷 is similar to 𝑋𝑌𝑍𝐿, what is the length of 𝐴𝐷?

Q2:

Given that triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar, work out the value of 𝑥.

  • A 𝑥 = 1 2
  • B 𝑥 = 7
  • C 𝑥 = 5
  • D 𝑥 = 2 . 5
  • E 𝑥 = 6

Q3:

If 𝐵𝐸𝐹𝐴𝐸𝐷𝐶𝐵, find the value of 𝑥.

Q4:

Given that 𝑄𝑅𝑃𝑀𝑆𝑉𝑍𝑊, find the value of 𝑥.

Q5:

Given that the two polygons are similar, find the value of 𝑥.

Q6:

These two shapes are similar, and their areas 𝐴 and 𝐴 are given. Find the value of 𝑥.

  • A3
  • B2
  • C2.5
  • D5

Q7:

Given that the two given polygons are similar, determine the value of 𝑥.

Q8:

Given that the two polygons are similar, find the value of 𝑥.

Q9:

Given that 𝐴𝐵𝐶𝐷𝐸𝐹𝐺𝐻, find the values of 𝑥 and 𝑦.

  • A 𝑥 = 1 6 , 𝑦 = 9
  • B 𝑥 = 1 6 , 𝑦 = 4
  • C 𝑥 = 1 0 , 𝑦 = 1 8
  • D 𝑥 = 8 , 𝑦 = 1 1
  • E 𝑥 = 8 , 𝑦 = 9

Q10:

Given that 𝐴𝐵𝐶𝐷𝑋𝑌𝑍𝐿, determine 𝑚𝑋𝑌𝑍.

Q11:

Given that 𝐴𝐵𝐶𝐷 is similar to 𝑄𝑆𝑅𝑃, find the values of 𝑥 and 𝑦.

  • A 𝑥 = 1 1 , 𝑦 = 4 9
  • B 𝑥 = 1 0 . 7 , 𝑦 = 4 6
  • C 𝑥 = 3 3 , 𝑦 = 4 9
  • D 𝑥 = 1 1 , 𝑦 = 4 6

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