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LenaWriter [7]
2 years ago
10

Find the area of triangle

Mathematics
1 answer:
liraira [26]2 years ago
8 0

So we see <u>one large triangle, that can be split into two triangles split by the thin dotted line</u>:

  • the<em> First triangle</em> --> has a hypotenuse of 26 and a leg of 11
  • the <em>Second triangle</em> --> has a hypotenuse of 42

Let us find the <u>other leg of the </u><u><em>First triangle</em></u> which also happens to be the <u>height of the larger triangle</u>, using the Pythagorean theorem

     a^2+b^2=c^2\\a^2 + 11^2 = 26^2\\a^2 = 26^2-11^2=555\\a=23.56

Thus the <u>height of the entire triangle</u> is 23.56 which also happens to be <u>one of the legs of the </u><u><em>Second triangle</em></u>

<em>      </em>a^2+b^2=c^2\\a^2+(23.56)^2=42^2\\a^2 = 1764-555=1209\\a = 34.77

Having found the other leg of the <em>Second Triangle</em>, we can find the base of the larger triangle is:

     -->  34.77 + 11 = 45.77

The height as found in the first initial step is 23.56 thus the area is

   Area = \frac{1}{2}*b*h=\frac{1}{2}*23.56*45.77=539.17

Hope that helps!

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