Question

In the given figure, if ar (∆ABC)=28cm^2
then ar (AEDF) =
(A) 21 cm^2
(B) 18 cm^2
(C) 16 cm^2
(D) 14 cm^2​

Answer 1

In the given figure, if ar (∆ABC)=28cm^2 then ar (AEDF) =

14 cm^2​

• Option (D) is correct.
• The sides of a smaller inscribed triangle are half in measure of those of a bigger triangle.
• Therefore the area of a smaller inscribed triangle is also half the value of the area of a bigger triangle.  
• Area of smaller inscribed triangle = Area of bigger triangle / 2
• Given,
• ar (∆ABC) = 28 cm^2
• ar (∆EDF) = 28 cm^2 / 2
• ∴ ar (∆EDF) = 14 cm^2

Answer 2

Answer:

The Area of AEDF is 14 cm² .

Step-by-step explanation:

Given as :

The Figure shows that ABC is triangle, and EDF is triangle inside it

The Area of Triangle  ΔABC = 28 cm²

Let The Area of Triangle  ΔEDF =  ΔADF = x cm²

Now,

Triangle ΔEDF = $\dfrac{1}{4}$ of ΔABC

So, Area of Triangle ΔDEF = ΔADF  =  $\dfrac{1}{4}$ × Area of Triangle ΔABC

Or, x = $\dfrac{1}{4}$ ×  28 cm²

Or, x = $\dfrac{28}{4}$

∴   x = 7 cm²

And The Area of AEDF = Area of Triangle ΔDEF + Area of Triangle ΔADF

Or, The Area of AEDF = 7 cm² + 7 cm² = 14 cm²

Hence , The Area of AEDF is 14 cm² . Answer