Question

Heron's formula: find the area of a triangle with sides a = 5, b = 8, and c = 11. use heron's formula. question 7 options: a) 18.33 b) 32.17 c) 20.88 d) 12.46

Answer 1

a

Explanation:

Heron's formula for calculating the area (A) of a triangle is

A =
`√(s(s-a)(s-b)(s-c))`

s is the semiperimeter and a, b, c are the side lengths

given a = 5, b = 8 and c = 11 , then

s =
`(a+b+c)/(2)` =
`(5+8+11)/(2)` =
`(24)/(2)` = 12

substitute these values into the formula for A

A =
`√(12(12-5)(12-8)(12-11))`

=
`√(12(7)(4)(1))`

=
`√(336)`

≈ 18.33 units² ( to 2 decimal places )