Answer:
20.3 square feet.
Step-by-step explanation:
We have been given the sides of a garden. We are asked to find the area of garden using Heron's formula.
The area of a triangle with sides a, b and c would be:
[tex]\text{Area of }\Delta=\sqrt{S(S-a)(S-b)(S-c)}[/tex], where S is the semi-perimeter of triangle.
Let us find semi-perimeter as:
[tex]S=\frac{6+7+8}{2}=\frac{21}{2}=10.5[/tex]
Substitute given side lengths:
[tex]\text{Area of garden}=\sqrt{10.5(10.5-6)(10.5-7)(10.5-8)}[/tex]
[tex]\text{Area of garden}=\sqrt{10.5(4.5)(3.5)(2.5)}[/tex]
[tex]\text{Area of garden}=\sqrt{413.4375}[/tex]
[tex]\text{Area of garden}=20.333162[/tex]
[tex]\text{Area of garden}\approx 20.3[/tex]
Therefore, the area of the garden would be 20.3 square feet.
