Worksheet: Equality of the Areas of Two Triangles

In this worksheet, we will practice identifying triangles having 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 𝑁 𝑀 𝐾 ?

  • A 𝐻 𝑁 𝐾 𝐶
  • B 𝑍 𝑂 𝑋 𝐻
  • C 𝐻 𝑁 𝑍
  • D 𝐶 𝑍 𝐻
  • E 𝐶 𝑁 𝐻

Q2:

Which triangle has the same area as 𝐿 𝐵 𝐶 ?

  • A 𝑂 𝑋 𝐿
  • B 𝐸 𝑂 𝐿
  • C 𝐸 𝐿 𝐵
  • D 𝐷 𝑋 𝐿
  • E 𝑂 𝑋 𝐷

Q3:

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

  • A 𝐶 𝐻 = 𝐷 𝐶
  • B 𝐶 𝐻 = 𝐻 𝐷
  • C 𝐶 𝐷 = 𝐹 𝐻
  • D 𝐶 𝐻 𝐹 𝐷

Q4:

If the area of 𝐷 𝐹 𝐶 = 9 3 . 8 c m 2 and 𝐴 𝐹 = 𝐹 𝐸 , find the area of 𝐴 𝐵 𝐸 .

Q5:

Which triangle has the same area as 𝐵 𝐿 𝐴 ?

  • A 𝐾 𝐶 𝐺
  • B 𝐶 𝐺 𝐵
  • C 𝐺 𝐵 𝐾
  • D 𝐾 𝑂 𝐿
  • E 𝐾 𝐶 𝐿

Q6:

If the areas of 𝐿 𝑁 𝐴 and 𝑌 𝐴 𝐺 are the same, which of the following must be true?

  • A 𝑌 𝐺 𝑁 𝐿
  • B 𝑌 𝐿 = 𝑁 𝐺
  • C 𝑌 𝐺 = 𝑁 𝐿
  • D 𝑌 𝐿 𝑁 𝐺
  • E 𝐴 𝑁 = 𝐴 𝐺

Q7:

Which triangle has the same area as 𝐴 𝐹 𝑀 ?

  • A 𝑀 𝐺 𝑍
  • B 𝐴 𝐹 𝑍
  • C 𝐹 𝑀 𝐺
  • D 𝐴 𝐹 𝐺
  • E 𝐴 𝑀 𝐺

Q8:

Which triangle has the same area as 𝐷 𝐶 𝑁 ?

  • A 𝐿 𝑀 𝐷
  • B 𝑂 𝐿 𝐷
  • C 𝑂 𝐷 𝐶
  • D 𝐹 𝑀 𝐷
  • E 𝐿 𝑀 𝐹

Q9:

If the areas of 𝑌 𝐴 𝐵 and 𝐹 𝐵 𝑁 are the same, which of the following must be true?

  • A 𝐹 𝑁 𝐴 𝑌
  • B 𝐹 𝑌 = 𝐴 𝑁
  • C 𝐹 𝑁 = 𝐴 𝑌
  • D 𝐹 𝑌 𝐴 𝑁
  • E 𝐵 𝐴 = 𝐵 𝑁

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