Answer:
302.02 units²
Step-by-step explanation:
To do this, we can first solve for the height of the trapezoid. We can do this using sin:
sin 70= [tex]\frac{x}{14}[/tex]
14· sin 70≈13.16
Now, we can solve for the base of the small triangle on the right by:
cos 70= [tex]\frac{x}{14}[/tex]
14 · cos 70 ≈4.79
Now, find the area of the triangle using [tex]V= \frac{1}{2} bh[/tex]:
V= (4.79)(13.16)/2≈30.86
Now, we can find the area of the rectangle in the middle by:
15· 13.16 (the height)= 197.4
Now, we need to solve for the triangle on the left. We will need to first find the base by subtracting the bases of the other figures from 31:
31-4.79-15= 11.21
Now, find the area of the triangle:
V=(11.21)(13.16)/2= 73.76
Add all of the areas, giving you:
73.76+30.86+197.4= 302.02 units²
