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.
Similar Questions
- 4 angles of a pentagon are $70^\circ$, $110^\circ$, $135^\circ$ and $95^\circ$. Find the measure of the fifth angle of the pentagon.
- If the perimeter of a square is 20 cm, then what is its area?
- If the difference between the exterior and the interior angles of a regular polygon is $60^{\circ}$, with an interior angle being greater than the corresponding exterior angle, then find the number of sides of the polygon.
- Find the area of an equilateral triangle whose perimeter is 24 cm.
- The area of the greatest circle that can be inscribed inside a square of side 21cm is:
- The floor of a hall is rectangular. Its length is 30 m and breadth is 24 m. How many carpets of size 6m $\times$ 4m are required to cover it?
The sum of all interior angles of a regular polygon is 1800°. How many diagonals does the polygon have?
The difference between the measure of an interior angle and an exterior angle of a regular polygon is 100°. What is the number of sides of the polygon?
- The length of a rectangular plot is twice its breadth and the length of its diagonal is $6\sqrt{5}$ m. The perimeter of the plot is ______.
- The length of each side of a regular hexagon is $2\sqrt{3} \text{ cm}$. What is the area of the given hexagon?
Important Questions from Plane Figures
If the area of a square is 625 cm 2, then what is the perimeter of the square?
The area and the perimeter of a sheet of paper are 240 cm 2and 68 cm, respectively. What would be its length and breadth?
One side of rectangular field is 15 meters and one of its diagonals is 17 meters. Then find the area of the field.
The bisector of ∠B in ΔABC meets AC at D. If AB = 12 cm, BC = 18 cm and AC = 15 cm, then the length of AD (in cm) is:
The perimeter and the length of one of the diagonals of a rhombus is 26 cm and 5 cm respectively. Find the length of its other diagonal (in cm).
