Maths-

General

Easy

Question

# Find the area of the shaded region.

Hint:

- Area of rectangle is given by product of length and breadth.
- Area of rectangle = length × breadth.
- Area of rectangle = l × b

## The correct answer is: Hence, Area of shaded region is 4x3 – x2 – 14x + 6.

### Answer:

- Step by step explanation:
- Given:

Length of outer rectangle = 4x – 2 units.

Width of outer rectangle = x^{2} – 3 units.

Length of inner rectangle = x units.

Width of inner rectangle = x + 2 units.

- Step 1:
- Find area of outer rectangle.

Area of rectangle = l × b

Area of rectangle = (4x – 2) × (x^{2} – 3)

Area of rectangle = 4x × (x^{2} – 3) – 2 (x^{2} – 3)

Area of rectangle = 4x^{3} – 12x – 2x^{2} + 6

Area of rectangle = 4x^{3}– 2x^{2} – 12x + 6

- Step 2:
- Find area of outer rectangle.

Area of rectangle = l × b

Area of rectangle = (x) × (x + 2)

Area of rectangle = (x^{2} + 2x)

- Step 3:
- Find area of shaded region:

Area of shaded region = area of outer rectangle – area of inner rectangle

Area of shaded region = (4x^{3}– 2x^{2} – 12x + 6) – (x^{2} + 2x)

Area of shaded region = (4x^{3}) – (2x^{2} + x^{2}) – (12x + 2x) + 6

Area of shaded region = 4x^{3} – x^{2} – 14x + 6

- Final Answer:

Hence, Area of shaded region is 4x^{3} – x^{2} – 14x + 6.

- Given:

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