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# In the diagram, \$ABCD\$ and \$EFGD\$ are squares each of area 16. If \$H\$ is the midpoint of both \$BC\$ and \$EF\$, find the total area of polygon

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In the diagram, \$ABCD\$ and \$EFGD\$ are squares each of area 16. If \$H\$ is the midpoint of both \$BC\$ and \$EF\$, find the total area of polygon \$ABHFGD\$.

michaelcai  Aug 25, 2017

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The side of each square must be of length 4 ( to give areas of 16). The length of HC is therefore 2, as is that of BH.

Imagine a line from H to D.  Triangle HCD has area (1/2)*2*4 = 4.  Similarly triangle HDE has area 4. Hence area of polygon HCDE is 8.

Area of polygon ABHED is therefore 16 - 8 = 8

Add this to the area of square DEFG to get a total area of 16 + 8 = 24 for polygon ABHFGD.

Alan  Aug 25, 2017
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#1
+26096
+2

The side of each square must be of length 4 ( to give areas of 16). The length of HC is therefore 2, as is that of BH.

Imagine a line from H to D.  Triangle HCD has area (1/2)*2*4 = 4.  Similarly triangle HDE has area 4. Hence area of polygon HCDE is 8.

Area of polygon ABHED is therefore 16 - 8 = 8

Add this to the area of square DEFG to get a total area of 16 + 8 = 24 for polygon ABHFGD.

Alan  Aug 25, 2017

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