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Solution - In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = 1/4ar (ABC). - CBSE Class 9 - Mathematics

ConceptTriangles on the Same Base and Between the Same Parallels

Question

In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = 1/4ar (ABC).

Solution

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal areas.

∴ Area (ΔABD) = Area (ΔACD)

⇒ Area (ΔABD) = 1/2Area (ΔABC)... (1)

In ΔABD, E is the mid-point of AD. Therefore, BE is the median.

∴ Area (ΔBED) = Area (ΔABE)

⇒ Area (ΔBED) = 1/2Area (ΔABD)

⇒ Area (ΔBED) = 1/2*1/2Area (ΔABC) [From equation (1)]

⇒ Area (ΔBED) = 1/4Area (ΔABC)

Is there an error in this question or solution?

APPEARS IN

 NCERT Mathematics Textbook for Class 9 (with solutions)
Chapter 9: Areas of Parallelograms and Triangles
Q: 2 | Page no. 162

Reference Material

Solution for question: In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = 1/4ar (ABC). concept: null - Triangles on the Same Base and Between the Same Parallels. For the course CBSE
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