ABC is a triangle in which D is the mid point of BC and E is the mid point of AD

A. The area of ∆ABC is equal to 4 times the area of ∆BED.
B. The area of ∆ADC is twice the area of ∆BED.
C. The area of ∆ADC is 4 times the area of ∆BED.
D. The area of ∆ABC is twice the area of ∆BED
Choose the correct answer from the options given below.

Correct option is D

Given:

ABC is a triangle in which D is the mid point of BC and E is the mid point of AD

Concept Used:

Median divides a triangle into two equal pieces with equal area.

Solution:

As given in the question,

AD is the median of the triangle ABC, so

Area of ∆ABD = Area of ∆ADC = $$\frac{1}{2} \text{ of Area of } \triangle ABC$$​​

Now, BE is the median of ∆ABD, so

Area of ∆BED = $$\frac{1}{2} \text{ of Area of } \triangle ABD = \frac{1}{2} \text{ of Area of } \triangle ADC$$​​

So, Area of ∆BED $$= \frac{1}{4} \text{ of Area of } \triangle ABC$$​​