Question

find the area of the trapezoid shown below area =

Explanation:

Step1: Identify trapezoid parameters

The two parallel sides (bases) are $b_1=2$ (length of the left side at $x=1$) and $b_2=5$ (length of the right side at $x=3$). The height (distance between the two bases) is $h=3-1=2$.

Step2: Apply trapezoid area formula

The formula for the area of a trapezoid is $A=\frac{1}{2}(b_1+b_2)h$. Substitute the values:
$A=\frac{1}{2}(2+5)\times2$

Step3: Calculate the final area

Simplify the expression:
$A=\frac{1}{2}\times7\times2=7$

Answer:

7