Find the area of polygon MNOPQR if MP = 9 cm, MD = 7 cm, MC = 6 cm, MB = 4 cm, MA = 2cm. NA, QC, QD and RB are perpendiculars to diagonal MP.

Solution

Area of polygon MNOPQR
= $ar space left parenthesis increment space MAN right parenthesis space plus space ar space left parenthesis trap. space ACON right parenthesis space plus space ar space left parenthesis increment space OCP right parenthesis space plus space ar space left parenthesis increment space PDQ right parenthesis plus space ar space left parenthesis trap. space DBRQ right parenthesis space plus space ar space left parenthesis increment space RBM right parenthesis$
∵ Area of $increment space MAN$ = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
= $1 half cross times 2 cross times AN space cm squared space equals space AN space cm squared$
Area of trapezium ACON = $1 half left parenthesis AN plus OC right parenthesis cross times AC$
$equals space 1 half left parenthesis AN plus OC right parenthesis space cross times space left parenthesis MC minus MA right parenthesis$
$equals space 1 half left parenthesis AN plus OC right parenthesis space cross times space left parenthesis 6 minus 2 right parenthesis$
$equals space 1 half left parenthesis AN plus OC right parenthesis cross times 4 space equals space 2 left parenthesis AN plus OC right parenthesis cm squared$