Answer:
The final answer is 32[tex]\sqrt{3}[/tex].
Step-by-step explanation:
The right triangle is a 30-60-90 triangle. Since we know that the hypotenuse of the triangle is 8, we can use the ratios to establish that the short leg is 4 and the long leg is 4[tex]\sqrt{3}[/tex].
The length of the rectangle is 10ft minus the base of the triangle or 10-4 = 6ft. We can then say that the area of the rectangle is 24[tex]\sqrt{3}[/tex] ft.
Next, since we know the base and height of the triangle we can use the formula 1/2 b*h to determine that the triangle is 8[tex]\sqrt{3}[/tex].
Finally, we add the areas together to a final answer of 32[tex]\sqrt{3}[/tex]
