Let x be the length of each side of the nonagon. We then split up the nonagon into 9 congruent, isosceles triangles, each with base = x and height = 12. Then the area of each triangle is 1/2 • x • 12 = 6x, so the total area of the nonagon will be 9 • 6x = 54x.
To find x, we can use some facts from geometry and trigonometry.
• In any polygon, the sum of the measures of the exterior angles is 360°. So each of these exterior angles will measure 360°/9 = 40°.
• Exterior angles are supplementary to the interior angles. So each interior angle will measure 180° - 40° = 140°.
• Each of the 9 triangles are isosceles with base angles measuring half the interior angles of the nonagon, 140°/2 = 70°.
• Cut the triangle in half along the labeled inradius of the nonagon, which has length 12. In the resulting right triangle, we have
tan(70°) = 12 / (x/2)
and solving for x gives
tan(70°) = 24/x
x = 24/tan(70°)
x = 24 cot(70°) ≈ 8.7
Then the total area of the nonagon is
54x = 54 • 24 cot(70°) ≈ 471.7
Step-by-step explanation:
No of miles a day = 5.75 miles
No of miles after 5 days = 5.75 x 5 = 28.75 miles
<span>Each sphere of ice has a radius of 2cm
</span>one tray makes 6 spheres
<span>What is the total volume of ice the tray can make at one time?
Total volume of each sphere is </span><span>33.51 cm^3
The tray can hold 6 of these at a time
33.5 * 6
201 cm^3 total volume of ice that the tray can make at one time
Written in pi
64

cm^3
Hope this helps :)</span>