Question

unit 1 test a ib applications sl block: ____ name: ____ 13. find the area of the shape below. 14. find the value of x.

Explanation:

Step1: Identify the shape for area calculation

The first - given shape is a trapezoid. The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height.
The lengths of the parallel sides are $a=33$ in and $b = 33+3.5 + 3.5=40$ in, and the height $h = 5$ in.

Step2: Calculate the area of the trapezoid

$A=\frac{(33 + 40)\times5}{2}=\frac{73\times5}{2}=\frac{365}{2}=182.5$ square inches.

Step3: For the right - triangle problem

In right - triangle $\triangle FGE$, we know an angle $\angle G = 71^{\circ}$ and the adjacent side to $\angle G$ is $FG = 8.1$. We want to find the hypotenuse $x$.
We use the cosine function $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(71^{\circ})=\frac{8.1}{x}$.

Step4: Solve for $x$

$x=\frac{8.1}{\cos(71^{\circ})}$. Since $\cos(71^{\circ})\approx0.3256$, then $x=\frac{8.1}{0.3256}\approx24.9$.

Answer:

1. Area of the shape: $182.5$ square inches
2. Value of $x$: approximately $24.9$