Question

The following exercise uses Heron's formula. Find the area of a garden that is a triangle with sides 6 feet, 7 feet, and feet. (Round your answer to one decimal place)

Answer 1

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:

$\text{Area of }\Delta=\sqrt{S(S-a)(S-b)(S-c)}$, where S is the semi-perimeter of triangle.

Let us find semi-perimeter as:

$S=\frac{6+7+8}{2}=\frac{21}{2}=10.5$

Substitute given side lengths:

$\text{Area of garden}=\sqrt{10.5(10.5-6)(10.5-7)(10.5-8)}$

$\text{Area of garden}=\sqrt{10.5(4.5)(3.5)(2.5)}$

$\text{Area of garden}=\sqrt{413.4375}$

$\text{Area of garden}=20.333162$

$\text{Area of garden}\approx 20.3$

Therefore, the area of the garden would be 20.3 square feet.