Question

Find the area of the trapezoid. Round your answer to the nearest tenth.C10 in. D14 in.ABin²h=60°in AB =in A=

Answer 1

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

`Area=(1)/(2)(a+b)h`

STEP 2: Write the given sides

`\begin{gathered} a=CD=10in \\ b=BA=? \\ h=? \end{gathered}`

STEP 3: find the side AB

To get x from the included right-angled triangle, we use the cosine function as seen below:

`\begin{gathered} \cos60=(x)/(14) \\ x=14*\cos60 \\ x=14*0.5=7 \end{gathered}`

Therefore, the value of:

`AB=10+7=17in`

STEP 4: Find the height of the trapezoid

Using Pythagoras theorem,

`\begin{gathered} h^2=14^2-7^2 \\ h^2=147 \\ h=√(147)=12.12435565 \\ h\approx12.1in \end{gathered}`

The height is approximately 12.1 inches

STEP 5: Find the area

By substitution,

`\begin{gathered} Area=(1)/(2)*(10+17)*√(147) \\ Area=0.5*27*12.1 \\ Area=163.35 \\ Area\approx163.4in^2 \end{gathered}`

Hence, the area of the trapezoid is approximately 163.4in²