Question

9.
The rectangle in the figure has an area equal to 640 cm. The points B are F are the mid points
of the sides AC and AE respectively. What is the area of the triangle BDF in cm ?
(A) 100 cm
(B) 320 cm
(C) 240 cm
(D) 160 cm​

Answer 1

Answer:

Let ABCD is a rectangle in which AB= CD = 2a units. BC=AD= 2b units. E is the

mid point of BC therefore BE= CE= b units and F is the midpoint of CD so that

CF= DF = a units.

Area of rectangle ABCD =2a×2b = 4.a.b units ^2…………………….(1)

Area of ∆ AEF= area of rectangle ABCD-area of (∆ABE+∆ADF+∆FCE).

3 units ^2= 4.a.b units ^2 - (2a×b/2+a×2b/2+a×b/2)units ^2.

or. 3. = 4.a.b. - (5/2).a.b

or. 3. = 3.a.b/2

or. 3.a.b= 6. => a.b. = 2. ………………..(2)

Putting a.b. = 2 from eqn. (2) in (1)

Area of rectangle ABCD = 4.a.b units ^2. = 4×2. = 8. unit ^2. Answer