Question

This figure consists of a rectangle and a quarter circle.

What is the perimeter of this figure?

Use 3.14 for π.

Enter your answer as a decimal in the box

Answer 1

To calculate the perimeter of the figure consisting of a rectangle and a quarter circle, we need to consider each part separately.

Let's assume the rectangle has a width \( w \) and a height \( h \). The quarter circle has a radius equal to the width \( w \) of the rectangle.

### Step 1: Calculate the perimeter of the rectangle

When considering the perimeter of the rectangle, we only count the two vertical sides and one horizontal side that are not part of the quarter circle:
\[
P_{\text{rectangle}} = 2h + w
\]

### Step 2: Calculate the circumference of the quarter circle

The circumference of a full circle is given by the formula:
\[
C = 2\pi r
\]
For a quarter circle:
\[
C_{\text{quarter circle}} = \frac{1}{4} \times 2\pi w = \frac{\pi w}{2}
\]
Using \( \pi \approx 3.14 \):
\[
C_{\text{quarter circle}} \approx \frac{3.14 w}{2} = 1.57 w
\]

### Step 3: Combine the perimeters

Finally, the total perimeter \( P \) of the figure is the sum of the perimeter of the rectangle and the length of the quarter circle:
\[
P = P_{\text{rectangle}} + C_{\text{quarter circle}}
\]
So,
\[
P = (2h + w) + (1.57 w)
\]
\[
P = 2h + w + 1.57w
\]
\[
P = 2h + 2.57w
\]

### Final Calculation

To find the exact numerical value of the perimeter, substitute the values of \( h \) and \( w \) as needed. If specific dimensions are provided for the rectangle, please share them to calculate the final perimeter value.