Question

write a polynomial expression that represents the area of a trapezoid with bases of 6x-5 and 4x+7, and a height of x+1.​

Answer 1

Answer:

A = 5x² + 6x + 1

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = $\frac{1}{2}$ h (a + b)

where h is the height and a, b the parallel bases, thus

A = $\frac{1}{2}$ (x + 1)(6x - 5 + 4x + 7)

   = $\frac{1}{2}$ (10x + 2)(x + 1)

   = (5x + 1)(x + 1) ← distribute using FOIL

   = 5x² + 6x + 1