Question

The recreation department of a small town wants to over-seed anarea of the local park, shown in the diagram. If it takes one5-pound bag of seed to cover 3000 square feet, how many bagsof seed will they need?

Answer 1

They need 17 bags of seed.

Step-by-step explanation:

First, lets divide the diagram in 3 parts and calculate the area for each part:

Part 1 (on the left of the diagram) - triangle

The base (b) of the triangle measures 320-240 = 80 feet

The height (h) of the triangle measures 75*2 (diameter of the half circle) = 150 feet

The area (At) of the triangle is:

At = (b*h)/2

At = (80*150)/2

At = 6000 square feet

Part 2 (on the middle of the diagram) - rectangle

The length (l) of the rectangle is 240 feet

The width (w) of the rectangle is 150 feet

The area (Ar) of the rectangle is:

Ar = l*w

Ar = 240*150

Ar = 36000 square feet

Part 3 (on the right of the diagram) - half circle

The radius of the circle is 75 feet

The area (Ac) of half the circle is:

Ac = πr²/2

Ac = π*(75)²/2

Ac = 2812.5π

Considering π=3.14

Ac = 8831 square feet

The total area of the figure is the sum of the areas:

Atotal = At + Ar + Ac

Atotal = 6000 + 36000 + 8831

Atotal = 50831

Now, we can calculate how many bags will be required

We know that

1 bag - 3000 square feet

Then

x - 50831

3000x = 50831

x = 50831/3000

x = 16.94

x = 17

They need 17 bags of seed.