What is the area of ABC below? If necessary, round your answer to two decimal places.

Question

anonymous · Answer

http://assets.openstudy.com/updates/attachments/512698f2e4b0111cc68f0a35-danny_boy-1361484031066-0e1a4ef912784612b2bd359ab3389ed5.gif

bahrom7893 · Answer

Area is (1/2)*base*height

bahrom7893 · Answer

base is :
AD + DC

jhannybean · Answer

Lets start by figuring out line DC first. In order to that we an utilize the pythagorean theorem.

bahrom7893 · Answer

sorry :3

jhannybean · Answer

lol np.

bahrom7893 · Answer

keep going

jhannybean · Answer

$\large DC^2 = BC^2 - BD^2$
$\large DC^2 = (23.2)^2 - (7.9)^2$

$\large DC = \sqrt{(23.2)^2-(7.9)^2}$
$\large DC =? $

anonymous · Answer

DC=21.813

jhannybean · Answer

Right, or $\large \sqrt{475.83}$.

jhannybean · Answer

Now we're going to use the pythagorean theorem on the other, smaller triangle. Remember, we can use this special theorem because line BD is a perpendicular bisector of   line AC,creating a 90 degree angle.

For the second triangle, we have 

$\large AD^2 = (9.4)^2 - (7.9)^2$

$\large AD = \sqrt{(9.4)^2 -(7.9)^2}$

$\large AD = ?$

anonymous · Answer

√ 25.95 or 5.094

jhannybean · Answer

Good!

jhannybean · Answer

Now to get the base, we add AD + BC together.

$\large AD+BC = \sqrt{475.83}+\sqrt{25.95} \approx 26.90764216$ 
That gives us the closest approximation to our base.

jhannybean · Answer

Now, the area of a triangle follows the formula 

$\large A = \frac12\cdot b\cdot h$

$\large b \approx 26.90764216$

$\large h = 7.9$

$\large A = \frac12 \cdot (26.90764216)\cdot (7.9)$

$\large A =?$

anonymous · Answer

A=106.28265

anonymous · Answer

but it tells me to round my answer to two decimal places if necessary

jhannybean · Answer

Ok. so we look at 106.28"2" The third decimal place . If the digit is above 5,round up,if below, keep it the same.

So we have A= 106.282, and since 2 is smaller than 5,we will keep our digits the same. A = 106.28

anonymous · Answer

thank you! :D

jhannybean · Answer

np :)

Remember to always keep the exact values of each variable you are trying to find before inputting your variables into your equations. Having the exact variable value helps in finding the exact answer,(hence why i kept the base length a really long number).