Question

the area of the square is 4x2-2x-6 square units A triangle inside the square has an area x2-4x+5 square units find the area of the shaded portion

Answer 1

Square area = 4x^2 -2x - 6 square units

Triangle area = x^2 - 4x + 5

shaded portion = (4x^2 -2x - 6) - ( x^2 - 4x + 5 )

= 3x^2 + 2x - 11

Answer 2

Given:

The area of a square $4x^{2} -2x-6$  and the triangle inside the square has an area $x^{2} -4x+5$.

To find:

The area of the shaded portion.

Solution:

The area of the shaded portion is found by subtracting the total area from the overlapping area of the figure. Here the actual figure is square and a triangle is inscribed by it. So, to find the shaded area, the area of the triangle is subtracted from the area of the square.

Subtract the area of the triangle from the area of the square.

$4x^{2} -3x-6-(x^{2} -4x+5)=4x^{2} -3x-6-x^{2} +4x-5\\=3x^{2} +x-11$

Thus, the area of the shaded portion is$3x^{2} +x-11$.