minmacurafinaa
22.04.2021 •
Mathematics
Question 11
Find the total surface area of this cone. Round to the nearest hundredth.
14,8 cm
15 cm
1667.91 cm squared
f
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Ответ:
1.260
Step-by-step explanation:
Each time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we add another 180° to the total:
If it is a Regular Polygon (all sides are equal, all angles are equal)
ShapeSidesSum of
Interior AnglesShapeEach Angle
Triangle3180°regular triangle60°
Quadrilateral4360°regular quadrilateral90°
Pentagon5540°pentagon regular108°
Hexagon6720°hexagon regular120°
Heptagon (or Septagon)7900°heptagon refular128.57...°
Octagon81080°octagon regular135°
Nonagon91260°nonagon regular140°
Any Polygonn(n−2) × 180°regular n gon(n−2) × 180° / n
So the general rule is:
Sum of Interior Angles = (n−2) × 180°
Each Angle (of a Regular Polygon) = (n−2) × 180° / n
Perhaps an example will help:
Example: What about a Regular Decagon (10 sides) ?
regular decagon
Sum of Interior Angles= (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°
And for a Regular Decagon:
Each interior angle = 1440°/10 = 144°
Note: Interior Angles are sometimes called "Internal Angles"