Question

If h = 10 cm, c = 6 cm, b = 12 cm, d = 4 cm, find the values of each of its parts separately and add to find the area WXYZ. Verify it by putting the values of h, a and b in the expression
$fraction numerator straight h left parenthesis straight a plus straight b right parenthesis over denominator 2 end fraction.$

Solution

Area of $increment PWZ space equals space 1 half ch space equals space 1 half cross times 6 cross times 10 space cm squared space equals space 30 space cm squared$
Area of $increment space QXY space equals space 1 half dh space equals space 1 half cross times 4 cross times 10 space cm squared space equals space 20 space cm squared$
Area of rectangle PQYZ = Length x Breadth = b x h
= 12 x 10 cm² = 120 cm²∴ Area of trapezium WXYZ = Area of $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ + Area of angle $space increment space QXY$ + Area of rectangle PQYZ
= 30 cm² + 20 cm² + 120 cm²
= 170 cm²
Also, area of trapezium WXYZ = $fraction numerator straight h left parenthesis straight a plus straight b right parenthesis over denominator 2 end fraction$
= $fraction numerator 10 left parenthesis 22 plus 12 right parenthesis over denominator 2 end fraction cm squared$
(∵ a = c + b +d
= 6cm + 12cm + 4 cm
= 22 cm)
= $space space space space fraction numerator 10 cross times 34 over denominator 2 end fraction cm squared space equals space 170 space cm squared$
Hence, the area of trapezium is verified.

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