Question

pls tell me the answer to this question.

Answer 1

FIGURE :

$\setlength{ \unitlength}{20} \begin{picture}(3,5) \linethickness{70} \put(1, 1){\line(0, 1){5}} \linethickness{20}\put(1, 5.5){\line(1, 0){5}} \linethickness{20} \put(5.5,1 ){\line(0,1 ){4}} \linethickness{15}\put(1, 1.36){\line(1, 0){5}} \linethickness{1}\put(3, 3.5){\vector(0,1 ){1}}\put(3, 2.8){\vector(0, - 1 ){1}}\put(3.5,4.8){\vector( - 1, 0){0.7}}\put(4.2, 4.8){\vector(1,0 ){0.7}}\put(3.6,4.7 ){ \tt x }\put(2.8,3 ){ \tt 5x - 2 }\put( - 1.5, 3.5){ \tt 5x }\put(2,6.25 ){ \tt 3x + 2 }\put(6, 6){\boxed{ @The Pathetic }} \end{picture}$

GIVEN :

• A figure with two rectangles, inner and outer , which creates a region whose area is to found.

TO FIND :

• The area of shaded region.

SOLUTION :

So, We need to take the regular formula of area of a rectangle.

• Area of a Rectangle = Length × Breadth

Firstly , we need to determine the area of the outermost rectangle.so, taking the formula here , and solving it a bit, it goes like :-

➠Area of outer Rectangle = (5x) * (3x + 2)

➠Area of outer Rectangle = (5x * 3x + 5x × 2)

➠Area of outer Rectangle = ( 15x + 10x )

➠Area of outer Rectangle = 25x

Now, we need to find the area of smaller or inner rectangle,

➠Area of inner Rectangle = (5x - 2) * (x)

➠Area of inner Rectangle = (x * 5x - x * 2)

➠Area of inner Rectangle = ( 5x - 2x)

➠Area of inner Rectangle = 3x

So, as we have found the area of both of the rectangles, we need to Subtract the area inner rectangle from the area of the outer rectangle to get the area of the shaded region, subtracting both would go like :-

➠Area of shaded region = (Area of outer rectangle) - (Area of inner rectangle)

➠Area of shaded region = (25x) - (3x)

➠Area of shaded region = 22x

Hence, The area of the shaded region is 22x