PYQ Vault
EbooksTutor

Triangle joining the midpoints has one-fourth the area (repeated)

This type of question, asked 4 times: CDS 2 2016, CDS 1 2017, CDS 1 2019, CDS 2 2023. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    56
    In an equilateral triangle another equilateral triangle is drawn inside joining the mid-points of the sides of given equilateral triangle and the process is continued up to 7 times. What is the ratio of area of fourth triangle to that of seventh triangle ?

    Tap an option to check your answer.

  2. Question 2

    CDS 1 2017

    76
    Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is 5 square units, then the area of the triangle PQR is

    Tap an option to check your answer.

  3. Question 3

    CDS 1 2019

    44
    Suppose PP, QQ and RR are the mid-points of sides of a triangle of area 128 cm2^2. If a triangle ABCABC is drawn by joining the mid-points of sides of triangle PQRPQR, then what is the area of triangle ABCABC ?

    Tap an option to check your answer.

  4. Question 4

    CDS 2 2023

    56
    ABC is a triangle with sides AB = 41 cm, BC = 28 cm and CA = 15 cm. If D, E and F are the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF ?

    Tap an option to check your answer.