ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AE respectively. If area of ΔABC is 16 cm², find the area of ΔDEF.
Answers
Concept : Median of the triangle divides it into two equal triangles.
Given : ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AE respectively. Area of ΔABC is 16 cm².
Let, AD is median of triangle ABC
ar (∆ADC) = ½ ar(∆ABC)
ar (∆ADC) = ½ × 16
[Given : ar(∆ABC)]
ar (∆ADC) = 8 cm² ………(1)
Now, AE is a median of ∆ADC.
ar (∆AED) = ½ ar (∆ADC)
ar (∆AED) = ½ × 8
[From eq 1]
ar (∆AED) = 4 cm² ……….(2)
Again, DF is the median of ∆AED
ar (∆DEF) = ½ ar(∆AED)
ar (∆DEF) = ½ × 4
[From eq 2]
ar (∆DEF) = 2 cm²
Hence, the area of ΔDEF is 2 cm².
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Answer:-
Concept :
Median of the triangle divides it into two equal triangles.
Given :
ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AE respectively. Area of ΔABC is 16 cm².
Let, AD is median of triangle ABC
ar (∆ADC) = ½ ar(∆ABC)
ar (∆ADC) = ½ × 16
[Given : ar(∆ABC)]
ar (∆ADC) = 8 cm² ………(1)
Now,
AE is a median of ∆ADC.
ar (∆AED) = ½ ar (∆ADC)
ar (∆AED) = ½ × 8
[From eq 1]
ar (∆AED) = 4 cm² ……….(2)
Again, DF is the median of ∆AED
ar (∆DEF) = ½ ar(∆AED)
ar (∆DEF) = ½ × 4
[From eq 2]
ar (∆DEF) = 2 cm²
Hence, the area of ΔDEF is 2 cm².
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