Answer:
see explanation
Step-by-step explanation:
area of Δ ABC is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 4x - 6 and h = 2x - 3 , then
A = [tex]\frac{1}{2}[/tex] (4x - 6)(2x - 3) ← expand using FOIL
= [tex]\frac{1}{2}[/tex](8x² - 24x + 18) ← distribute
= 4x² - 12x + 9
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Area of rectangle CBFG is calculated as
A = lb ( l is length, b is breadth )
Here l = 4x - 6 and b = 3x - 2, then
A = (4x - 6)(3x - 2) ← expand using FOIL
= 12x² - 26x + 12
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Area of trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases
Here h = 2x - 3, b₁ = 4x + 1, b₂ = 2x + 3 , then
A = [tex]\frac{1}{2}[/tex] (2x - 3)(4x + 1 + 2x + 3)
= [tex]\frac{1}{2}[/tex] (2x - 3)(6x + 4) ← expand using FOIL
= [tex]\frac{1}{2}[/tex] (12x² - 10x - 12) ← distribute
= 6x² - 5x - 6
