Question

Ted with his friend Ned, was watching Mission Impossible. It was the climax scene, Ethan Grunt jumping from an airplane 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 swampy area. And the total area is area of parallelogram from which we have to subtract swampy area.

From the figure,
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 – AF = 70 m – 30 m = 40 m

This means FBED is a square.

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

= (70 $\times$ 40) – (40 $\times$ 40)

= (2800 – 1600) $m^2$

= 1200 $m^2$