Question

1. Find the exact value for area of the triangle with the side lengths 5, 9, and 10.

Answer 1

area = 6
`√(14)` units²

Explanation:

Given the 3 sides of a triangle, we can use Hero's formula to calculate the area (A)

A =
`√(s(s-a)(s-b(s-c))`

where s s the semi perimeter and a, b , c the sides of the triangle

let a = 5, b = 9 and c = 10

s =
`(a+b+c)/(2)` =
`(5+9+10)/(2)` =
`(24)/(2)` = 12

A =
`√(12(12-5)(12-9)(12-10))`

=
`√(12(7)(3)(2))`

=
`√(504)`

=
`√(36(14))`

= 6
`√(14)` units²

Answer 2

Explanation:

a = 5 units ; b = 9units ; c = 10 units

Semi perimeter = (a+b+c)/2 = (5+9+10)/2 = 24/2 = 12 units

s-a = 12 -5 = 7 units

s -b = 12 - 9 = 3 units

s-c = 12- 10 =2 units

`Area=√(s*(s-a)(s-b)(s-c))\\\\=√(12*7*3*2)\\\\=√(2*2*3*7*3*2)\\\\=2*3√(2*7)\\\\=6√(14)\\`

=6*3.742 = 22.452

= 22.45 square units