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Question

The mid points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to ________.


Solution

Given: 
ABC is a triangle


Let D is the mid-point of ABE is the mid-point of BC and F is the mid-point of AC.

ADEF is a parallelogram having 2 triangles of equal area i.e., ∆ADF and ∆DEF.

But the ∆ABC is divided in 4 triangles of equal area i.e., ∆ADF, ∆DEF, ∆BED and ∆CEF.

Thus, area of ∆ABC = × area of the parallelogram ADEF.


Hence, the mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to half the area of the triangle ABC.

Mathematics
RD Sharma (2019)
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