In terms of x, find an expression that represents the area of the shaded region. The outer square has side lengths of (x+5) and the inner square has side lengths of (x-2), as shown.

Can someone help me with this?

needmathhelp
Apr 7, 2017

#1**+3 **

Is it like this?

(The position of the red square inside the blue square doesn't matter.)

To find the area of the shaded region, all we need to do is find the area of the bigger, blue square, and subtract from it the area of the smaller, red square.

shaded area = blue square area - red square area

blue square area = side^{2} = (x + 5)^{2}

red square area = side^{2} = (x - 2)^{2}

shaded area = (x + 5)^{2} - (x - 2)^{2}

shaded area = (x + 5)(x + 5) - (x - 2)(x - 2)

shaded area = [x^{2} + 10x + 25] - [x^{2} - 4x + 4]

shaded area = x^{2} + 10x + 25 - x^{2} + 4x - 4

**shaded area = 14x + 21 sq. units.**

hectictar
Apr 7, 2017