Polygon Angle Sum Calculation
To find the sum of the interior angles of a polygon, we use a specific formula based on the number of sides.
Interior Angle Sum Formula
The formula for the sum of the interior angles of a polygon with n sides is:
$ \text{Sum} = (n-2) \times 180^\circ $
Applying the Formula
In this question, the polygon has 11 sides. So, we set n = 11.
- Substitute the value of n into the formula:
$ \text{Sum} = (11-2) \times 180^\circ $
- Calculate the value inside the parentheses:
$ \text{Sum} = 9 \times 180^\circ $
- Perform the multiplication:
$ \text{Sum} = 1620^\circ $
Conclusion
The sum of the interior angles of a polygon with 11 sides is $1620^\circ$. This matches Option 4.
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Important Questions from Plane Figures
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
The width of the path around a square field is 4.5 m and its area is 105.75 m 2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
What is the area of the square (in cm 2) whose vertices lie on a circle of radius 5 cm?
The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m 2) of the path is:
Take \(\left(\pi=\frac{22}{7}\right)\)
