Question

Need help ASAP What is the area of this triangle Enter your answer as a decimal in the box

Answer 1

Answer:

$\boxed{A=43.54cm^2}$

Step-by-step explanation:

To find this area we will use the law of cosine and the Heron's formula. First of all, let't find the unknown side using the law of cosine:

$x^2=12^2+8^2-2(12)(8)cos(65^{\circ}) \\ \\ x^2=144+64-192(0.42) \\ \\ x^2=208-80.64 \\ \\ x^2=127.36 \\ \\ x=\sqrt{127.36} \\ \\ \therefore \boxed{x=11.28cm}$

Heron's formula (also called hero's formula) is used to find the area of a triangle using the triangle's side lengths and the semiperimeter. A polygon's semiperimeter s is half its perimeter. So the area of a triangle can be found by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ being $a,\:b\:and\:c$ the corresponding sides of the triangle.

So the semiperimeter is:

$s=\frac{12+8+11.28}{2} \\ \\ s=15.64cm$

So the area is:

$A=\sqrt{15.64(15.64-12)(15.64-8)(15.64-11.28)} \\ \\ \therefore \boxed{A=43.54cm^2}$