Question

Ted with his friend Ned, was watching Mission Impossible. It was the climax scene, Ethan jumping from an aeroplane during the night. With the help of his gadgets, he got a blueprint of a parallelogram-shaped land he was about to land on and its measurements. Find the area of the place he can land to cheat death one more time by not falling in the rectangular killer swamp!

• A. 1200 $m^2$
• B. 1600 $m^2$
• C. 900 $m^2$
• D. 1000 $m^2$

Answer 1

The correct option is A

1200 $m^2$

Ethan can land on the area other than the swamp. The total area is the area of parallelogram from which we have to subtract the area of the swamp.

We know that one of the sides of the swamp is 40 m. We have to find the other side in order to find the area of the swamp.

AD = BC = 50 m [Opposite sides of a parallelogram]

Using Pythagoras Theorem,

$A{D}^2=F{D}^2+A{F}^2$

2500 = 1600 + $A{F}^2$

$A{F}^2$ = 900

AF = 30 m

So, the other side of the swamp = BF = AB – FB = 70 m – 30 m = 40 m

This means FBED is a square.

So, the area Ethan can land = Area of parallelogram – Area of the square

= (70 $\times$ 40) – (40 $\times$ 40)

= (2800 – 1600) $m^2$

= 1200 $m^2$