Question

Ted with his friend Ned, was watching Mission Impossible. It was the climax scene, Ethan Grunt jumping from an-air plane during night. With the help of his gadgets, he got a blue print 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 m²
• B. 1600 m²
• C. 900 m²
• D. 1000 m²

Answer 1

The correct option is A

1200 m²

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

We know that one of the sides of the swampy area 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 – AF = 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 $m^2$