Find S of a right-angled triangle whose hypotenuse is 313 and one of the legs is 312.

A rectangular triangle is a triangle in which one of the angles is 90º.

In order to calculate the area of ​​a given triangle, you need to find the length of the second leg. To do this, apply the Pythagorean theorem:

AB ^ 2 = BC ^ 2 + AC ^ 2;
AC ^ 2 = AB ^ 2 – BC ^ 2;
AC ^ 2 = 313 ^ 2 – 312 ^ 2 = 97969 – 97344 = 625;
AC = √625 = 25 cm.

To calculate the area of ​​a triangle, we will use Heron’s Formula:

S = √p (p – a) (p – b) (p – c); Where:

S is the area of ​​the triangle;

p – semi-perimeter (p = P / 2);

a – side AB;

b – aircraft side;

c – speaker side;

p = (313 + 312 + 25) / 2 = 650/2 = 325 cm;

S = √325 (325 – 313) (325 – 312) (325 – 25) = √325 12 13 300 = √15210000 = 3900 cm2.

Answer: the area of ​​the triangle is 3900 cm2.