# How do you find the area of a triangle ABC, if a = 23, b = 46 , and c = 41?

Mar 12, 2018

Area of the triangle is $470.914$ sq.unit.

#### Explanation:

In triangle DeltaABC ; a= 23 , b=46 , c=41

The semi perimeter of triangle is $s = \frac{a + b + c}{2}$ or

$s = \frac{23 + 46 + 41}{2} = 55$ unit

Area of the triangle is A_t=sqrt(s(s-a)(s-b)(s-c) or

A_t=sqrt(55(55-23)(55-46)(55-41) or

${A}_{t} = \sqrt{55 \cdot 32 \cdot 9 \cdot 14} = \sqrt{221760} \approx 470.914$ sq.unit

Area of the triangle is $470.914$ sq.unit. [Ans]