Worksheet: Equality of the Areas of Two Triangles

In this worksheet, we will practice identifying triangles that have the same area when their bases are equal in length and the vertices opposite to these bases are on a parallel line to them.

Q1:

Which of the following has the same area as 𝑁𝑀𝐾?

  • A𝐻𝑁𝑍
  • B𝐶𝑁𝐻
  • C𝑍𝑂𝑋𝐻
  • D𝐻𝑁𝐾𝐶
  • E𝐶𝑍𝐻

Q2:

Which triangle has the same area as 𝐿𝐵𝐶?

  • A𝐷𝑋𝐿
  • B𝑂𝑋𝐷
  • C𝐸𝐿𝐵
  • D𝐸𝑂𝐿
  • E𝑂𝑋𝐿

Q3:

Points 𝑍, 𝐻, and 𝐷 are collinear. If the areas of 𝑍𝐶𝐻 and 𝐶𝐻𝐷 are the same, which of the following must be true?

  • A𝐶𝐻=𝐷𝐶
  • B𝐶𝐻𝐹𝐷
  • C𝐶𝐻=𝐻𝐷
  • D𝐶𝐷=𝐹𝐻

Q4:

If the area of 𝐷𝐹𝐶=93.8cm and 𝐴𝐹=𝐹𝐸, find the area of 𝐴𝐵𝐸.

Q5:

Which triangle has the same area as 𝐵𝐿𝐴?

  • A𝐾𝑂𝐿
  • B𝐾𝐶𝐺
  • C𝐶𝐺𝐵
  • D𝐺𝐵𝐾
  • E𝐾𝐶𝐿

Q6:

If the areas of 𝐿𝑁𝐴 and 𝑌𝐴𝐺 are the same, which of the following must be true?

  • A𝑌𝐿=𝑁𝐺
  • B𝑌𝐿𝑁𝐺
  • C𝐴𝑁=𝐴𝐺
  • D𝑌𝐺=𝑁𝐿
  • E𝑌𝐺𝑁𝐿

Q7:

Which triangle has the same area as 𝐴𝐹𝑀?

  • A𝐴𝐹𝑍
  • B𝑀𝐺𝑍
  • C𝐴𝑀𝐺
  • D𝐹𝑀𝐺
  • E𝐴𝐹𝐺

Q8:

Which triangle has the same area as 𝐷𝐶𝑁?

  • A𝐹𝑀𝐷
  • B𝐿𝑀𝐹
  • C𝑂𝐷𝐶
  • D𝑂𝐿𝐷
  • E𝐿𝑀𝐷

Q9:

Which of the following has the same area as 𝐾𝑂𝑁𝑍?

  • A𝐹𝑂𝐿𝐴
  • B𝐾𝐹𝐿𝑁
  • C𝐾𝐴𝐿
  • D𝐾𝐹𝐿𝑁𝑂
  • E𝐾𝐹𝐿

Q10:

Given that the area of 𝐷𝑀𝑌𝐶=68cm and 𝐵𝑋=𝐶𝑌, find the area of 𝐴𝑀𝑋𝐵.

Q11:

Given that 𝐵𝑁𝐴𝑀, which of the following has the same area as 𝐴𝐵𝐶?

  • A𝐿𝐸𝑀
  • B𝐷𝐹𝑀𝐿
  • C𝐵𝐶𝐸𝐷
  • D𝐷𝐸𝑀𝐿
  • E𝐿𝑀𝑁

Q12:

Which of the following has the same area as 𝐷𝐸𝐵?

  • A𝐹𝐵𝐶
  • B𝐸𝐷𝐶
  • C𝐸𝐹𝐶
  • D𝐴𝐷𝐹𝐸
  • E𝐷𝐵𝐶𝐸

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