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 :

$s = \frac{1}{2} \times (8x + 2)(6x) - (x)(3x + 1)$

$s = \frac{1}{2} \times (48 {x}^{2} + 12x) - (3 {x}^{2} + x)$

$s = \frac{48}{2} {x}^{2} + \frac{12}{2} x - 3 {x}^{2} - x$

$s = 24 {x}^{2} + 6x - 3 {x}^{2} - x$

$s = 24 {x}^{2} - 3 {x}^{2} + 6x - x$

$s = 21 {x}^{2} + 5x$

And we're done

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