Question

Basil N. Thyme is putting in a triangular herb garden with sides of 2 yards, 3 yards and 4 yards. He needs to know the area of his garden so he would know how many herb plants to germinate in his greenhouse.. What is the area of his herb garden to the nearest square foot? (convert yards to feet.)

Answer 1

26.14 ft²

1) Considering that triangular herb:

2) Let's calculate the area of that triangle using the Heron formula so that we can not need to find the height:

2.1) Calculate the Perimeter:

2P = 2+3+4

2P = 9 yd

2 yards = 6 ft

3 yd = 9ft

4 yd = 12 ft

Converting into feet

9 yards = 27 feet

And the Semi perimeter (half the perimeter):

P = 9/2

27/2

Now we can plug that into Heron's Formula:

$\begin{gathered} A=\sqrt[]{p(p-a)(p-b)(p-c)} \\ A=\sqrt[]{\frac{27}{2}(\frac{27}{2}-6))(\frac{27}{2}-9)(\frac{9}{2}-12)} \\ A=\frac{27\sqrt[]{15}}{4}\approx26.14 \end{gathered}$

3)

So the area of that triangular garden is approximately 26.14 ft²