9514 1404 393
Answer:
1) 135°
2) 0.77 units
3) 0.92 units
4) 6.12 units
5) 2.83 square units
Step-by-step explanation:
1) The exterior angle at any vertex is 360°/n, where n is the number of sides. For the octagon, the exterior angle is 360°/8 = 45°. The interior angle will be the supplement of this: 180° -45° = 135°.
The measure of each interior angle is 135°.
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2) Each sector of the octagon is an isosceles triangle with a central angle of 45° (also 360°/8). Since the radius is 1 unit, the length of one side is twice the sine of half the central angle.
s = 2·sin(45°/2) ≈ 0.765367
The length of one side is about 0.77 units.
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3) Similarly, the apothem is the cosine of half the central angle:
a = cos(45°/2) ≈ 0.923880
The apothem is about 0.92 units.
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4) For an octagon, the perimeter is 8 times the length of one side.
P = 8s = 8(0.765367) ≈ 6.12293
The perimeter is about 6.12 units.
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5) The area of one sector (isosceles triangle) is given by the formula ...
A = (1/2)bh
A = 1/2sa ≈ 1/2(0.765367)(0.923880) ≈ 0.353553
Then the area of the octagon is 8 times this:
A = 8(sector area) = 8(0.353553) ≈ 2.82843
The octagon area is about 2.83 square units.
So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter
Hope this helped!
Answer:
5cm^3
Step-by-step explanation: please let me know if that wrong.
Answer:
8.275
Step-by-step explanation:
8.280 - 8.270 = 0.010
0.010/2 = 0.005
8.270 + 0.005 = 8.275
