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Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

 Jun 12, 2024
 #1
avatar+1952 
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We can use a really handy formula to help solve this question. 

 

First, we have to calculate the semiperimeter of the triangle, which is half the sum of the three side.

We get 3+4+62=132

 

That may seem useless, but it will come in handy very soon. 

 

Now, we apply Heron's Formula, which states that the area of a triangle is equal to s(sa)(sb)(sc). Subbing everything in, We get

Area=132(1323)(1324)(1326)

Area=45516=4554

 

So our final answer is 4554

 

Thanks! :)

 Jun 12, 2024

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