Area of room

Geometry Level 2

The diagram shows the floor plan of a room. Adjacent walls are perpendicular to each other. Letters a and b represent the lengths of some the walls. What is the area of the room?

3 a ( b − a ) + a 2 3a(b - a) + a^2 3 a b 3ab 2 a b 2ab 3 a ( a + b ) − a 2 3a(a + b) - a^2 2 a b + a ( b − a ) 2ab + a(b - a)

Munem Shahriar by Munem Shahriar , 18, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

The top right a × a a\times a square can be placed into the bottom empty part, as is shown in the figure. (The placing is possible, since the emty part and the top right square are congurent.)

Hence the new generated rectangle's area is equal to the yellow decagon's area. The sides of the rectangle are b b and a + a + a = 3 a a+a+a=3a , so its area is b × 3 a = 3 a b b\times 3a=\boxed{3ab}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Consider the diagram.

A r e a ( r o o m ) = A r e a ( b i g r e c t a n g l e ) − A r e a ( 2 s m a l l r e c t a n g l e s ) = ( b + a ) ( 3 a ) − a ( 2 a ) − a ( a ) = 3 a b + 3 a 2 − 2 a 2 − a 2 = Area_{(room)}=Area_{(big~rectangle)}-Area_{(2~small~rectangles)}=(b+a)(3a)-a(2a)-a(a)=3ab+3a^2-2a^2-a^2= 3 a b \boxed{3ab}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...