Question

The area of a trapezoid is found using the formula A-½ h(b1+b2), where A is the area, h is the height, and b1 and b2 are the lengths of the bases. What is the area of a trapezoid with the height of 12, b1 = x + 1, and b2 = x + 3?

Answer 1

Given, h=12.

b1=x+1.

b2=x+3.

The area of the trapezoid is,

$\begin{gathered} A=\frac{1}{2}h(b_1+b_2) \\ =\frac{1}{2}\times12(x+1)(x+3) \\ =6(x+1)(x+3) \\ =6(x^2+3x+x+3) \\ =6(x^2+4x+3) \\ =6x^2+6\times4x+6\times3 \\ =6x^2+24x+18 \end{gathered}$

Therefore, the area of the trapezoid is,

$6x^2+24x+18$

Hence, option C is correct.