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

Answer:

7 m^2

Step-by-step explanation:

$s = \dfrac{a + b + c}{2}$

$A = \sqrt{s(s - a)(s - b)(s - c)}$

$s = 6$

$\dfrac{a + b + c}{2} = 6$

$a = b = c$

$\dfrac{a + a + a}{2} = 6$

$3a = 12$

$a = b = c = 4$

$A = \sqrt{6(6 - 4)(6 - 4)(6 - 4)}$

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

$A = \sqrt{48}$

$A = 6.92820...$

$A = 7~m^2$

Answer 2

Answer:

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

Step-by-step 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 =   $\frac{x+x+x}{2}$

                          $\frac{3x}{2}=6$

                          $3x=12$

                          $x=4$

By Heron's formula,

$Area=\sqrt{s(s-a)(s-b)(s-c)}$

           $=\sqrt{6(6-4)(6-4)(6-4)}$

           $=\sqrt{6\times2\times2\times2}$

           $=\sqrt{48}$

           $=4\sqrt{3}$

           $=4\times1.73$

           $=6.92$

           $=7\:m^2\:(approx.)$

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