Question

Find the area of the shaded region
need this ASAP!

Answer 1

ALL THE SHAPES HERE ARE RECTANGLES AND THE AREA OF A RECTANGLE IS =L×B

TO GET THE AREA OF THE SHADED PART WE SAY THE AREA OF THE OUTSIDE SHAPE SUBTRACT THE AREA OF THE INNER SHAPE.

LET US FIND THE AREA OF THE OUTSIDE RECTANGLE FIRST.

`a1 = (x + 5)(x - 1) \\ = {x}^(2) - x + 5x - 5 \\ a = {x}^(2) +4 x - 5`

NOW LET US FIND THE AREA OF THE INNER RECTANGLE.

`a2 = (x + 1)(x - 4) \\ a = {x}^(2) - 4x + x - 4 \\ \\ a = {x }^(2) - 3x - 4`

the area of the shaded part is given by

`a1 - a2 = ( {x}^(2) +4 x - 5) - ( {x}^(2) - 3x - 4) \\ = {x}^(2) + 4x - 5 - {x }^(2) + 3x + 4 \\ = {x}^(2) - {x}^(2) + 4x + 3x - 5 + 4 \\ areashaded = 7x - 1`