Question

Find the Area of the shaded part.

Answer 1

To find the area of the shaded part we have to subtract the rectangle area from the triangle area :

`s = (1)/(2) * (8x + 2)(6x) - (x)(3x + 1) \\`

`s = (1)/(2) * (48 {x}^(2) + 12x) - (3 {x}^(2) + x) \\`

`s = (48)/(2) {x}^(2) + (12)/(2) x - 3 {x}^(2) - x \\`

`s = 24 {x}^(2) + 6x - 3 {x}^(2) - x`

`s = 24 {x}^(2) - 3 {x}^(2) + 6x - x`

`s = 21 {x}^(2) + 5x`

And we're done

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