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
Answer:
answer is 1
Step-by-step explanation:
just did test on edge
Answer:
5 row, 3 left
Step-by-step explanation:
She has 48 flowers, 5 flowers one row
How many rows can she make? So divide
48/ 5
= 9.6
So she can only make 9 rows
The leftovers flowers are the flowers that didn't manage to make 5 per row
Therefore, if she can make 9 rows, in other words 9 x 5 = 45
45 flowers were able to be placed in a sequence of 5 per row
So the ones that are left is
48 - 45
= 3
Answer:
98°
Step-by-step explanation:
180° - 82° = 98°