First, I will re-sketch the image
First, we need to find x
Using the trig. ratio
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan 45=\frac{6}{x}[/tex]
cross-multiply
[tex]x\tan 45=6[/tex][tex]x\times1=6[/tex][tex]x=6[/tex]
Next, we need to find y
Using the trig. ratio
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex][tex]\sin 45=\frac{6}{y}[/tex]
cross-multiply
[tex]y\sin 45=6[/tex]
Divide both-side of the equation by sin45
[tex]y=\frac{6}{\sin 45}[/tex][tex]y=8.485[/tex]
Area of a trapezoid is given by the formula;
[tex]A=\frac{1}{2}(a+b)h[/tex]
From the sketch above,
a=12
b=24
h=6
substitute the value and then evaluate
[tex]A=\frac{1}{2}(12+24)6[/tex][tex]=108\text{ square unit}[/tex]
Perimeter is the distance around the shape
[tex]\text{Perimeter}=8.485+12+8.485+24[/tex][tex]\text{perimeter }\approx\text{ 53}[/tex]
