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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. - Mathematics

Answer in Brief

ABC is a triangle in which D is the mid-point of BCand F are mid-points of DC and AErespectively. IF area of ΔABC is 16 cm2, find the area of ΔDEF.

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Given: Here from the given question we get

(1) ABC is a triangle

(2) D is the midpoint of BC

(3) E is the midpoint of CD

(4) F is the midpoint of A

Area of ΔABC = 16 cm2

To find : Area of ΔDEF

Calculation: We know that ,

The median divides a triangle in two triangles of equal area. 

For ΔABC, AD is the median

Area of Δ ADC = `1/2 `(Area of ΔABC ) 

                        `=1/2 (16)`

                          = 8 cm2

Area of Δ ADC = 8cm2

For ΔADC , AE is the median .

Area of ΔAED = `1/2 `  (Area of Δ ABC)

                       `= 1/2 (8)`

                         = 4 cm2

Area of ΔAED =  4 cm2

Similarly, For ΔAED , DF is the median .

Area of ΔDEF = `1/2 `  (Area of Δ AED)

                       `= 1/2 (4)`

                         = 2 cm2

Area of ΔDEF =  2 cm2

Hence we get Area of ΔDEF2 cm2

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RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 7 | Page 60
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