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:
<ABC=50
<EDB=30
<DFC=60
Step-by-step explanation:
<ABC=50 BECAUSE ANGLE SUM PROPERTY
90+40+50=180
<EDB=30 BECUSE ANGLE SUM PROPERTY
100+50+30=180
<DFC=60 BECAUSE ANGLE SUM PROPERTY
30+90+50=180
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Answer:
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Step-by-step explanation:
Answer:
g(q) = 5/8q
Step-by-step explanation:
-7q + 12r = 3q - 4r
Add 4r to each side
-7q + 12r+4r = 3q - 4r+4r
-7q +16r = 3q
Add 7q to each side
-7q+7q +16r = 3q+7q
16r = 10q
Divide each side by 16
16r/16 = 10q/16
r = 5q/8
g(q) = 5/8q
First step:
simplify the values in the parenthesis:
-4(3+11v)
Second step:
apply the distributive property:
-12-44v
The final answer (simplified) is -44v-12