Question

A window seat is in the shape of a trapezoid. Write the polynomial that represents the area of the window seat.

Answer 1

The polynomial that represents the area of the trapezoid shaped window is: 1/2(8x² - 14x - 15).

What is the Area of a Trapezoid?

Area of trapezoid = 1/2(a + b)h, where a and b are length of the parallel sides, and h is the height.

Given:

a = 3x + 5

b = x - 2

h = 2x - 5

Thus:

Area of trapezoid = 1/2(3x + 5 + x - 2)(2x - 5)

Area of trapezoid = 1/2(4x + 3)(2x - 5)

Area of trapezoid = 1/2(8x² - 14x - 15)

Therefore, the polynomial that represents the area of the trapezoid shaped window is: 1/2(8x² - 14x - 15).

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