SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating the area of the trapezoid
[tex]Area=\frac{1}{2}(a+b)h[/tex]
STEP 2: Write the given sides
[tex]\begin{gathered} a=CD=10in \\ b=BA=? \\ h=? \end{gathered}[/tex]
STEP 3: find the side AB
To get x from the included right-angled triangle, we use the cosine function as seen below:
[tex]\begin{gathered} \cos60=\frac{x}{14} \\ x=14\times\cos60 \\ x=14\times0.5=7 \end{gathered}[/tex]
Therefore, the value of:
[tex]AB=10+7=17in[/tex]
STEP 4: Find the height of the trapezoid
Using Pythagoras theorem,
[tex]\begin{gathered} h^2=14^2-7^2 \\ h^2=147 \\ h=\sqrt{147}=12.12435565 \\ h\approx12.1in \end{gathered}[/tex]
The height is approximately 12.1 inches
STEP 5: Find the area
By substitution,
[tex]\begin{gathered} Area=\frac{1}{2}\times(10+17)\times\sqrt{147} \\ Area=0.5\times27\times12.1 \\ Area=163.35 \\ Area\approx163.4in^2 \end{gathered}[/tex]
Hence, the area of the trapezoid is approximately 163.4in²
