Answer:
(10x⁴ - 52x³ + 5x² + 246x - 196) ft²
Explanation:
The figure can be divided into two rectangles: the small rectangle and the large rectangle.
Dimensions of the small rectangle:
Length (l) = (x) ft
Width (w) = (x² - 6) - (5x - 14) = x² - 6 - 5x + 14 = (x² - 5x + 8) ft
Area of small rectangle = l*w = (x)(x² - 5x + 8)
Area = x(x²) - x(5x) + x(8) (using distributive property)
Area of small rectangle = (x³ - 5x² + 8x) ft²
Dimensions of large rectangle:
Length (l) = (2x³ - 5x² - 12x + 14) ft
Width (w) = (5x - 14) ft
Area of large rectangle = l*w = (2x³ - 5x² - 12x + 14)(5x - 14)
2x³(5x - 14) - 5x²(5x - 14) - 12x(5x - 14) + 14(5x - 14) (distributive property)
10x⁴ - 28x³ - 25x³ + 70x² - 60x² + 168x + 70x - 196
Combine like terms
Area of large rectangle = (10x⁴ - 53x³ + 10x² + 238x - 196) ft²
Area of figure = area of small rectangle + area of large rectangle
= (x³ - 5x² + 8x) + (10x⁴ - 53x³ + 10x² + 238x - 196)
Open parentheses
= x³ - 5x² + 8x + 10x⁴ - 53x³ + 10x² + 238x - 196
Combine like terms and arrange in standard form (from the greatest degree to the least)
= 10x⁴ + x³ - 53x³ - 5x² + 10x² + 8x + 238x - 196
= 10x⁴ - 52x³ + 5x² + 246x - 196
Area of the figure = (10x⁴ - 52x³ + 5x² + 246x - 196) ft²