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?

  • A β–³ 𝐻 𝑁 𝑍
  • B β–³ 𝐢 𝑁 𝐻
  • C 𝑍 𝑂 𝑋 𝐻
  • D 𝐻 𝑁 𝐾 𝐢
  • E β–³ 𝐢 𝑍 𝐻

Q2:

Which triangle has the same area as △𝐿𝐡𝐢?

  • A β–³ 𝐷 𝑋 𝐿
  • B β–³ 𝑂 𝑋 𝐷
  • C β–³ 𝐸 𝐿 𝐡
  • D β–³ 𝐸 𝑂 𝐿
  • E β–³ 𝑂 𝑋 𝐿

Q3:

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

  • A 𝐢 𝐻 = 𝐷 𝐢
  • B 𝐢 𝐻 βˆ₯ 𝐹 𝐷
  • C 𝐢 𝐻 = 𝐻 𝐷
  • D 𝐢 𝐷 = 𝐹 𝐻

Q4:

If the area of △𝐷𝐹𝐢=93.8cm and 𝐴𝐹=𝐹𝐸, find the area of △𝐴𝐡𝐸.

Q5:

Which triangle has the same area as △𝐡𝐿𝐴?

  • A β–³ 𝐾 𝑂 𝐿
  • B β–³ 𝐾 𝐢 𝐺
  • C β–³ 𝐢 𝐺 𝐡
  • D β–³ 𝐺 𝐡 𝐾
  • E β–³ 𝐾 𝐢 𝐿

Q6:

If the areas of △𝐿𝑁𝐴 and β–³π‘Œπ΄πΊ are the same, which of the following must be true?

  • A π‘Œ 𝐿 = 𝑁 𝐺
  • B π‘Œ 𝐿 βˆ₯ 𝑁 𝐺
  • C 𝐴 𝑁 = 𝐴 𝐺
  • D π‘Œ 𝐺 = 𝑁 𝐿
  • E π‘Œ 𝐺 βˆ₯ 𝑁 𝐿

Q7:

Which triangle has the same area as △𝐴𝐹𝑀?

  • A β–³ 𝐴 𝐹 𝑍
  • B β–³ 𝑀 𝐺 𝑍
  • C β–³ 𝐴 𝑀 𝐺
  • D β–³ 𝐹 𝑀 𝐺
  • E β–³ 𝐴 𝐹 𝐺

Q8:

Which triangle has the same area as △𝐷𝐢𝑁?

  • A β–³ 𝐹 𝑀 𝐷
  • B β–³ 𝐿 𝑀 𝐹
  • C β–³ 𝑂 𝐷 𝐢
  • D β–³ 𝑂 𝐿 𝐷
  • E β–³ 𝐿 𝑀 𝐷

Q9:

Which of the following has the same area as 𝐾𝑂𝑁𝑍?

  • A 𝐹 𝑂 𝐿 𝐴
  • B 𝐾 𝐹 𝐿 𝑁
  • C β–³ 𝐾 𝐴 𝐿
  • D 𝐾 𝐹 𝐿 𝑁 𝑂
  • E β–³ 𝐾 𝐹 𝐿

Q10:

Given that the area of π·π‘€π‘ŒπΆ=68cm and 𝐡𝑋=πΆπ‘Œ, find the area of 𝐴𝑀𝑋𝐡.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.