Question

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square feet, of ΔABC.

Options:

A)

7.385

B)

8.270

C)

6.495

D)

5.591

Answer 1

C)
`6.495\: ft^2`

Explanation:

a = 7 ft, b = 3 ft, c = 5 ft (Given)

Therefore, a + b + c = 7 + 3 + 5 = 15 ft

Let's calculate semi Perimeter of the triangle which is given by s

`s =(a+b+c)/(2)=(15)/(2) = 7.5 \: ft`

Now, by Heron's formula, area of triangle ABC is given as:

`A(\triangle ABC) =√(s(s-a) (s-b)(s-c))`

`\therefore A(\triangle ABC) =√(7.5(7.5-7) (7.5-3)(7.5-5))`

`\therefore A(\triangle ABC) =√(7.5(0.5) (4.5)(2.5))`

`\therefore A(\triangle ABC) =√(42.1875)`

`\therefore A(\triangle ABC) =6.49519053`

`\therefore A(\triangle ABC) =6.495\: ft^2`