Question

Exercise 21

Answer 1

Answer:

see explanation

Step-by-step explanation:

area of Δ ABC is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height )

Here b = 4x - 6 and h = 2x - 3 , then

A = $\frac{1}{2}$ (4x - 6)(2x - 3) ← expand using FOIL

   = $\frac{1}{2}$(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 = $\frac{1}{2}$ 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 = $\frac{1}{2}$ (2x - 3)(4x + 1 + 2x + 3)

   = $\frac{1}{2}$ (2x - 3)(6x + 4) ← expand using FOIL

   = $\frac{1}{2}$ (12x² - 10x - 12) ← distribute

   = 6x² - 5x - 6