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Question
CBSEENMA8003358
Wired Faculty App

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

(b) Write the perimeter of each shape.

Solution

(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. 
                                

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Question
CBSEENMA8003359
Wired Faculty App

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

Solution

(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.

Question
CBSEENMA8003360
Wired Faculty App

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.

Solution

∵  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

Question
CBSEENMA8003361
Wired Faculty App

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.]

Solution

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
                                              <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
                                               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
Also, perimeter of the 2 semicircles = <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
                                                         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
                                                           

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