Question

vidur needs to buy mulch for his garden. what is the area of his garden? use 3.14 for \\(\pi\\). round to the nearest hundredth if necessary. 5.5 yd

Explanation:

Step1: Recall the formula for the area of a semicircle

The area of a full circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle. For a semicircle, the area is half of the area of the full circle, so the formula for the area of a semicircle is \( A = \frac{1}{2} \pi r^2 \).

Step2: Identify the radius of the semicircle

From the diagram, the radius \( r \) of the semicircle is \( 5.5 \) yards.

Step3: Substitute the values into the formula

We are given that \( \pi \approx 3.14 \) and \( r = 5.5 \) yd. Substituting these values into the formula for the area of a semicircle:
\[
A = \frac{1}{2} \times 3.14 \times (5.5)^2
\]

Step4: Calculate \( (5.5)^2 \)

First, calculate \( 5.5 \times 5.5 = 30.25 \).

Step5: Multiply by \( 3.14 \)

Next, multiply \( 30.25 \) by \( 3.14 \):
\[
30.25 \times 3.14 = 94.985
\]

Step6: Multiply by \( \frac{1}{2} \)

Now, take half of \( 94.985 \):
\[
\frac{1}{2} \times 94.985 = 47.4925
\]

Step7: Round to the nearest hundredth (if necessary)

The value \( 47.4925 \) rounded to the nearest hundredth is \( 47.49 \) (since the thousandth place is \( 2 \), which is less than \( 5 \), we don't round up the hundredth place).

Answer:

The area of Vidur's garden is \( 47.49 \) square yards.