Question

TRIGONOMETRY Find the area of this triangle round to the nearest whole number

Answer 1

13,170 square units

Step-by-step explanation

The side lengths of this triangle are all different, so it is a scalene triangle. The three side lengths are given, so we will use the following formula to find the area,

`A=\sqrt[]{s(s-a)(s-b)(s-c)}`

Where a, b, and c, are the side lengths of the triangle, and s is the semi-perimeter,

`s=(a+b+c)/(2)`

In this case, the semi-perimeter is,

`s=(260+175+155)/(2)=(590)/(2)=295`

So the area is,

`A=\sqrt[]{295\cdot(295-260)\cdot(295-175)\cdot(295-155)}=\sqrt[]{295\cdot35\cdot120\cdot140}=\sqrt[]{173,460,000}\approx13,170`

Hence, the area of this triangle is 13,170 square units.