Question

24. Find the area of the shaded region:

Answer 1

5x^3+ 17x^2- 35x-30 Or x=-4.63 or 1.9

Explanation:

Area of rectangle =L×B

for smaller rectangle :

after applying the formula, the equation becomes:

6x^2 - 3x

For bigger rectangle:

Applying the same formula, the equation becomes:

5x^3+ 23x^2- 38x- 30

Area of shaded region =

Area of bigger rectangle- Area of smaller rectangle

= 5x^3+17x^2 -35x-30

going further solving the above equation

Area of shaded region: -4.96 or 1.9

Answer 2

A = 5x³ + 17x² - 35x - 30

Explanation:

the shaded area (A) is calculated as

A = outer area - inner area

= (5x + 3)(x² + 4x - 10) - 3x(2x - 1) ← distribute parenthesis

= 5x³ + 20x² - 50x + 3x² + 12x - 30 - (6x² - 3x)

= 5x³ + 23x² - 38x - 30 - 6x² + 3x ← collect like terms

= 5x³ + 17x² - 35x - 30