Question

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

Answer 1

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 ΔDEF =  2 cm²