Question

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

Answer 1

ANSWER

13,170 square units

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,

$s=\frac{a+b+c}{2}$

In this case, the semi-perimeter is,

$s=\frac{260+175+155}{2}=\frac{590}{2}=295$

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.