`DeltaABC` में BC,CA तथा AB के मध्य बिंदु क्रमश D,E तथा F हे तो समांतर चतुर्भुज DEFB के छेत्रफल तथा समलम्ब चतुर्भुज CAFD के छेत्रफल का अनुपात ज्ञात करे?

Options

A. `1:2`
B. `3:4`
C. `1:3`
D. `2:3`

Answer

D

Explanation

We know that whan a new triangle is formed by using mid points of big triangle.
`rArr ` In this case Area of 4 triangle is same

`rArr` i.e. Area of `DeltaAFE = DeltaFBD = DeltaFDE = DeltaDEC = 1`
`rArr` Parallelogram DEFB = `angleBFD + angleDFE = 1+1`
`rArr` Area of parallelorgam =2.............(i)
`rArr` Again trapezium CAFD
`rArr DeltaAFE + DeltaFED+DeltaDCE = 1+1+1`
Area of trapezium CAFD = 3 .............(ii)
Required Ratio will be `=2:3`