a painted design on a tile is composed of a trapezoid and a right triangle. the trapezoid has base, = 3.5 in and base, = 5.5 in with a height of 4 in. the height of the triangle measures 5.5 inches with the base of 6 inches. what is the total area of the painted design in square inches? in²

Question

Accepted Answer

# Explanation:
## Step1: Calculate the area of the trapezoid
The formula for the area of a trapezoid is $A_{t}=\frac{(b_1 + b_2)h}{2}$, where $b_1 = 3.5$ in, $b_2=5.5$ in, and $h = 4$ in.
$$
\begin{align*}
A_{t}&=\frac{(3.5 + 5.5)\times4}{2}\
&=\frac{9\times4}{2}\
&= 18
\end{align*}
$$
## Step2: Calculate the area of the triangle
The formula for the area of a triangle is $A_{tri}=\frac{1}{2}bh$, where $b = 6$ in and $h = 5.5$ in.
$$
\begin{align*}
A_{tri}&=\frac{1}{2}\times6\times5.5\
&=3\times5.5\
&=16.5
\end{align*}
$$
## Step3: Calculate the total area
The total area $A = A_{t}+A_{tri}$
$$
\begin{align*}
A&=18 + 16.5\
&=34.5
\end{align*}
$$

# Answer:
$34.5$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the area of the trapezoid

Step2: Calculate the area of the triangle

Step3: Calculate the total area

Answer: