Question

30.) for the purpose of purchasing lumber for a new fence and seed to plant grass, a.) find the area and perimeter of the yard below. image of right triangle with 27 ft (vertical leg), 36 ft (horizontal leg), 45 ft (hypotenuse) b.) identify whether a fence has to do with area or perimeter and the same with grass seed.

Explanation:

Part (a)

Step 1: Identify the shape and formulas

The yard is a right - triangle. For a right - triangle, the area formula is \(A=\frac{1}{2}\times base\times height\) and the perimeter formula is \(P = a + b+ c\) (where \(a\), \(b\), and \(c\) are the side lengths of the triangle). Here, the base \(b = 36\) ft, the height \(h=27\) ft, and the hypotenuse \(c = 45\) ft.

Step 2: Calculate the area

Using the area formula for a right - triangle \(A=\frac{1}{2}\times base\times height\). Substitute \(base = 36\) ft and \(height=27\) ft into the formula:
\(A=\frac{1}{2}\times36\times27\)
First, calculate \(36\times27 = 972\), then \(\frac{1}{2}\times972=486\) square feet.

Step 3: Calculate the perimeter

Using the perimeter formula for a triangle \(P=a + b + c\). Here, \(a = 27\) ft, \(b = 36\) ft, \(c = 45\) ft.
\(P=27 + 36+45\)
First, \(27+36 = 63\), then \(63 + 45=108\) feet.

• A fence is used to enclose the yard. The length of the fence needed is equal to the distance around the yard, which is the perimeter.
• Grass seed is spread over the surface of the yard. The amount of grass seed needed depends on the size of the surface, which is the area.

Answer:

(a):
The area of the yard is \(486\) square feet and the perimeter is \(108\) feet.

Part (b)