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Maths-

General

Easy

Question

Find the area of the shaded region.

hint 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 = x² – 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) × (x² – 3)
Area of rectangle = 4x × (x² – 3) – 2 (x² – 3)
Area of rectangle = 4x³ – 12x – 2x² + 6
Area of rectangle = 4x³– 2x² – 12x + 6

Step 2:

Find area of outer rectangle.

Area of rectangle = l × b
Area of rectangle = (x) × (x + 2)
Area of rectangle = (x² + 2x)

Step 3:

Find area of shaded region:

Area of shaded region = area of outer rectangle – area of inner rectangle
Area of shaded region = (4x³– 2x² – 12x + 6) – (x² + 2x)
Area of shaded region = (4x³) – (2x² + x²) – (12x + 2x) + 6
Area of shaded region = 4x³ – x² – 14x + 6

Final Answer:

Hence, Area of shaded region is 4x³ – x² – 14x + 6.

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