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In the figure below, isosceles triangle ABC with base AB has altitude CH = 24 cm, DE = GF, HF = 12 cm, and FB = 6 cm. find area of CDEFG

 Apr 21, 2021

Best Answer 

 #2
avatar+9299 
+3

 

By AA similarity, △GFB is similar to △CHB, just as you said  smiley

 

This means we can make the following equation:

 

GF / FB  =  CH / HB

                                      Now we can substitute  6  for  FB,  24 for  CH,  and  18  for HB

GF / 6   =   24 / 18

                                      Multiply both sides of the equation by  6

GF   =   (24 / 18)  *  6

                                      Simplify the right side of the equation

GF   =   8

 

 

Now we can find the area of  △GFB

 

area of △GFB   =   (1/2) * FB * GF   =   (1/2) * 6 * 8   =   24

 

We can see that because the left side of the big triangle is symmetrical to the right side, △GFB is congruent to  △DEA. (We can also say that since  m∠GBF = m∠DAE,    m∠GFB = m∠DEA,   and  DE = GF,  by AAS,  △GFB ≅  △DEA)

 

This means the area of △DEA is also 24 sq cm

 

Now we can find the area of △ABC.

 

area of △ABC  =  (1/2) * AB * CH  =  (1/2) * (2 * 18) * (24)  =  432

 

Now we can find the area of CDEFG.

 

area of CDEFG   =   area of △ABC  -  area of △GFB  -  area of △DEA

 

area of CDEFG   =   432  -  24  -  24

 

area of CDEFG   =   384   (and that is in sq cm)

 Apr 21, 2021
 #1
avatar+2118 
+1

Hello :))

 

I'm so obsessed with taylor swift rn. 

What's your favorite song?

So CHB = CHA (triangles are similar)

So we can just find FHCG and multiply by 2. 

CHB = 24*12/2 = 144

GFB/CHB = 6/24

So CHFG = 108

108*2 = 216

 

=^._.^=

 Apr 21, 2021
 #3
avatar+29 
+2

i like all songs- hardcore swiftie here😭

wbu? 

tayIorswift13  Apr 21, 2021
 #5
avatar+2118 
+2

oh no, it looks like I messed up. 

hectitar is completly right. 

 

I love taylor swift :DD

Like, I know all her songs by heart. 

My favorites are enchated, all too well, blank space, long live, mr perfectly fine, love story, champagne problems, you are in love, there are just too many to name.

 

=^._.^=

catmg  Apr 21, 2021
 #2
avatar+9299 
+3
Best Answer

 

By AA similarity, △GFB is similar to △CHB, just as you said  smiley

 

This means we can make the following equation:

 

GF / FB  =  CH / HB

                                      Now we can substitute  6  for  FB,  24 for  CH,  and  18  for HB

GF / 6   =   24 / 18

                                      Multiply both sides of the equation by  6

GF   =   (24 / 18)  *  6

                                      Simplify the right side of the equation

GF   =   8

 

 

Now we can find the area of  △GFB

 

area of △GFB   =   (1/2) * FB * GF   =   (1/2) * 6 * 8   =   24

 

We can see that because the left side of the big triangle is symmetrical to the right side, △GFB is congruent to  △DEA. (We can also say that since  m∠GBF = m∠DAE,    m∠GFB = m∠DEA,   and  DE = GF,  by AAS,  △GFB ≅  △DEA)

 

This means the area of △DEA is also 24 sq cm

 

Now we can find the area of △ABC.

 

area of △ABC  =  (1/2) * AB * CH  =  (1/2) * (2 * 18) * (24)  =  432

 

Now we can find the area of CDEFG.

 

area of CDEFG   =   area of △ABC  -  area of △GFB  -  area of △DEA

 

area of CDEFG   =   432  -  24  -  24

 

area of CDEFG   =   384   (and that is in sq cm)

hectictar Apr 21, 2021
 #4
avatar+29 
+2

thank you!

tayIorswift13  Apr 21, 2021

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