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Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m2.


∵  The given plot is a square with side as 25 m.
∴     Area of the plot = Side x Side
                                 = 25 m x 25 m = 625 m2
∵  The constructed portion is a rectangle having length = 20 m and breadth = 15 m.
∴     Area of the constructed portion = 20 m x 15 m
                                                          = 300 m2
                    Now area of the garden = [Total plot area] - [Total constructed area]
                                                           = (625 - 300)m2
                                                           = 325 m2
∴  Cost of developing the garden =  Rs 55 x 325
                                                     = Rs 17, 875

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(a) Match the following figures with their respective areas in the box.

(b) Write the perimeter of each shape.


(a)

(b) (i) The given figure is a rectangle in which
      Length = 14 cm
      Breadth = 7 cm
∵           Perimeter of a rectangle = 2 x [Length + Breadth]
∴        Perimeter of the given figure = 2 x [14 cm + 7 cm]
                                                       = 2 x 21 cm
                                                       = 42 cm
                                                                           
     (ii)  The figure is a square  housing its side as 7 cm.
           ∵                Perimeter of a square = 4 x side
           ∴         Perimeter of the given figure = 4 x 7 cm
                                                                    = 28 cm. 
                                
          

2482 Views

The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden. [Length of rectangle is 20 - (3.5 + 3.5) meters.]


For the semi-circular part:
Diameter of the semi-circle = 7 m
∴  Radius of the semi-circle = 7 over 2 equals 3.5 space straight m
     Area of the 2 semi-circles =space space space space 2 open square brackets 1 half πr squared close square brackets
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                                               equals 22 over 7 cross times 35 over 10 cross times 35 over 10 space straight m squared

                                               equals space fraction numerator 11 cross times 35 over denominator 10 end fraction straight m squared space equals space 38.5 space straight m squared

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                                                         equals space 2 cross times 22 over 7 cross times 35 over 10 space straight m
                                                          = 22 m
For rectangular part:
                            Length of the rectangle = 20 - (3.5 + 3.5) m
                                                                 = 13 m
                            Breadth of the rectangle = 7 m
∴                                                     Area = Length x Breadth
                                                                = 13 m x 7 m
                                                                = 91 m2
                                      Perimeter = 2 x [Length + Breadth]
                                                      = 2 x [13 m + 0 m]
                                        = 2 x  13 m
                                        = 26 m
Now, Area of the garden = (38.5 + 91)m2
                                        = 129.5 m2
Perimeter of the garden = 22 m + 26 m
                                      = 48 m
                                                           

2143 Views

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles area required to cover a floor of area 1080 m2?
(If required you can split the tiles in whatever way want to fill up the corners.)


Area of a parallelograms = Base x Corresponding height
                     Area of a tile =space space space space open parentheses 24 over 100 cross times 10 over 100 close parentheses straight m squared space equals space 240 over 10000 straight m squared space equals space 0.024 space straight m squared
∴         Area of the floor  = 1080 m2
         Now, number of tiles = fraction numerator Total space area over denominator Area space of space one space tiles end fraction

                                          = fraction numerator 1080 over denominator 0.024 end fraction
                                          = 45000 tiles

2124 Views

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?


(a) Side of the square = 60 m
∴        Its perimeter = 4 x side
                               = 4 x 60 m
                                = 240 m
             Area of the square = Side x Side
                                            = 60 m x 60 m
                                             = 3600 m2
(b) ∵   Perimeter of the rectangle = Perimeter of the given square
      ∴   Perimeter of the rectangle = 240 m
      or    2 x [Length + Breadth] = 240 m
      or    2 x [80 m + Breadth] = 240 m
       or               80 m + Breadth = 240 over 2 straight m space equals space 120 space straight m
        ∴                         Breadth  = (120 - 80) m = 40 m
        Now,               Area of the rectangle  = Length x Breadth
                                                                  = 80 m x 40 m
                                                                  = 3200 m2
         Since,  3600 m2 > 3200 m2
          ∴  Area of the square field (a) is greater.

940 Views