Mathematics
Grade9
Easy

Question

Find the area of the regular polygon.

  1. 250    
  2. 348    
  3. 340    
  4. 289    

hintHint:

Polygon is a two- dimensional closed figure which is made up of three or more line segments. Each polygon has its own properties based on the number of sides. Area of a regular polygon can be determined using the formula A r e a equals 1 half cross times P e r i m e t e r space o f space t h e space p o l y g o n cross times A p o t h e m . Here, we have to find the area of the given polygon.

The correct answer is: 289


    In the question there is a polygon as shown in the figure above.
    Here, we have to find the area of the given polygon.
    From the given figure we can say that,
    Length of each side= 6.84
    Firstly, we have to find the length of apothem.
    For that, consider apothem to be a.
    So, tan 70 = fraction numerator a over denominator 3.42 end fraction
    rightwards double arrow a= tan 70 × 3.42
    rightwards double arrow a=  9.39
    Now, we have to find the perimeter of the polygon.
    Perimeter= Length of each side of the polygon × No. of sides
    = 6.84×9
    Area = fraction numerator 1 over denominator 2 end fraction ×apothem ×Perimeter
    = fraction numerator 1 over denominator 2 end fraction ×9.39 × (9×6.84)
    = 289
    Thus, the area of the given polygon is 289.
    Therefore, the correct option is d, i.e., 289.

    A perpendicular line segment joining the centre and one of the sides of the regular polygon is called apothem of the polygon.

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