Calculate the perimeter of the composite figure shown in the image.

Question

ScanSolve AI Tutor · Accepted Answer

My apologies, Precious. I made an incorrect assumption in the previous response for 4.4. Let's correct it using the dimensions clearly visible in the image.

4.4

Identify the components of the figure and their dimensions.
The figure consists of a rectangular base and a semicircle on top.
The vertical side of the rectangular part is $47 \text{ mm}$ .
The horizontal side of the rectangular part (bottom) is $36 \text{ mm}$ .
The diameter of the semicircle is the width of the rectangular part, which is $36 \text{ mm}$ .
Calculate the perimeter.
The perimeter consists of:
- Two vertical sides of the rectangle: $47 \text{ mm} + 47 \text{ mm}$
- The bottom horizontal side of the rectangle: $36 \text{ mm}$
- The arc length of the semicircle: $\frac{1}{2} \times \pi \times \text{diameter}$
The formula for the arc length of a semicircle is $L = \frac{1}{2} \pi d$ , where $d$ is the diameter.
Here, $d = 36 \text{ mm}$ .
$P = 47 \text{ mm} + 47 \text{ mm} + 36 \text{ mm} + \frac{1}{2} \pi (36 \text{ mm})$ $P = 130 \text{ mm} + 18 \pi \text{ mm}$
Using $\pi \approx 3.14159$ :
$P \approx 130 \text{ mm} + 18 \times 3.14159 \text{ mm}$ $P \approx 130 \text{ mm} + 56.54862 \text{ mm}$ $P \approx 186.54862 \text{ mm}$
Rounding to two decimal places:
$P \approx 186.55 \text{ mm}$
The perimeter of the figure is $\text{186.55 mm}$ .

Calculate the perimeter of the composite figure shown in the image.

Answer

Step-by-step solution

Identify the components of the figure and their dimensions.

Calculate the perimeter.

Try one yourself

Still stuck on this one?

More Mathematics Questions