Question

Heron’s formula: Area = An equilateral triangle has a semiperimeter of 6 meters. What is the area of the triangle? Round to the nearest square meter. 2 square meters 7 square meters 20 square meters 78 square meters

Answer 1

7 m^2

Explanation:

`s = (a + b + c)/(2)`

`A = √(s(s - a)(s - b)(s - c))`

`s = 6`

`(a + b + c)/(2) = 6`

`a = b = c`

`(a + a + a)/(2) = 6`

`3a = 12`

`a = b = c = 4`

`A = √(6(6 - 4)(6 - 4)(6 - 4))`

`A = \sqrt{6(2)^3`

`A = √(48)`

`A = 6.92820...`

`A = 7~m^2`

Answer 2

Option 2 is correct that is area of triangle is 7 m².

Explanation:

Given: Equilateral Triangle is given.

Semi Perimeter of triangle = 6

To find: Area of the triangle

Let, Side of equilateral triangle be x

Semi Perimeter, s =
`(x+x+x)/(2)`

`(3x)/(2)=6`

`3x=12`

`x=4`

By Heron's formula,

`Area=√(s(s-a)(s-b)(s-c))`

`=√(6(6-4)(6-4)(6-4))`

`=√(6*2*2*2)`

`=√(48)`

`=4√(3)`

`=4*1.73`

`=6.92`

`=7\:m^2\:(approx.)`

Therefore, Option 2 is correct that is area of triangle is 7 m².