Question

Nick wants to build an herb garden in the backyard but is only using the area beyond the path running through the yard. How large would the garden be if it istriangular-shaped with sides of length 10 feet, 7 feet, and 9 feet? Round to the nearest hundredth.

Answer 1

Given:

The sides of the triangular shape are 10 feet, 7 feet, and 9 feet.

Aim:

We need to find the area of the triangle.

Step-by-step explanation:

let a = 10 feet, b =7 feet and c =9 feet.

Consider the formula to find the area of the triangle.

`A=√(s\left(s-a\right)\left(s-b\right)\left(s-c\right))`

where s is the semi perimeter of the triangle.

The formula to find the semi perimeter.

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

Substitute a =10 feet, b =7 feet, and c = 9 feet.

`s=(10+7+9)/(2)`

`s=13`

Substitute s =13, a =10 feet, b =7 feet, and c = 9 feet.

`A=√(13\left(13-10\right)\left(13-7\right)\left(13-9\right))`

`A=√(13*3*6*4)`

`A=√(936)`
`A=30.59\text{ feet }^2`

Final answer:

`A=30.59\text{ feet }^2`