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:
No solutions
Step-by-step explanation:
31 times any positive number cannot be a negative number.
Answer:
When a habitat is destroyed, the carrying capacity for indigenous plants, animals, and other organisms is reduced so that populations decline, sometimes up to the level of extinction. Habitat loss is perhaps the greatest threat to organisms and biodiversity.
Step-by-step explanation:
x = 10
since GI bisects ∠DGH then ∠DGI = ∠IGH, hence
2x - 13 = x - 3 ( subtract x from both sides )
x - 13 = - 3 ( add 13 to both sides )
x = 10
Answer:y=-1/3x+14
Step-by-step explanation: