Find the perimeter. 25 cm

Question

ScanSolve AI Tutor · Accepted Answer

To find the perimeter of the given shape, we need to sum the lengths of all its sides.

Identify the components of the perimeter.
The image shows a shape with three straight sides and one curved side.
We assume the shape is composed of three sides of a square and a semi-circular base.
The top straight side is given as $25 \text{ cm}$ .
Based on the drawing, the two vertical straight sides are also $25 \text{ cm}$ each.
The bottom curved side appears to be a semi-circle with a diameter equal to the length of the top side, which is $25 \text{ cm}$ .
Calculate the total length of the straight sides.
There are three straight sides, each measuring $25 \text{ cm}$ .
$\text{Total length of straight sides} = 3 \times 25 \text{ cm} = 75 \text{ cm}$
Calculate the length of the curved side (semi-circle arc).
The formula for the circumference of a full circle is $C = \pi d$ , where $d$ is the diameter. For a semi-circle, the arc length is half of the full circumference.
The diameter of the semi-circle is $25 \text{ cm}$ .
$\text{Arc length} = \frac{1}{2} \times \pi \times d$ $\text{Arc length} = \frac{1}{2} \times \pi \times 25 \text{ cm}$ $\text{Arc length} = 12.5 \pi \text{ cm}$
Using the approximation $\pi \approx 3.14159$ :
$\text{Arc length} \approx 12.5 \times 3.14159 \text{ cm} \approx 39.27 \text{ cm}$
Calculate the total perimeter.
The total perimeter is the sum of the lengths of the straight sides and the curved side.
$\text{Perimeter} = \text{Total length of straight sides} + \text{Arc length}$ $\text{Perimeter} = 75 \text{ cm} + 12.5 \pi \text{ cm}$
Substituting the approximate value for the arc length:
$\text{Perimeter} \approx 75 \text{ cm} + 39.27 \text{ cm}$ $\text{Perimeter} \approx 114.27 \text{ cm}$
The perimeter of the shape is $114.27 \text{ cm}$ .

Find the perimeter. 25 cm

Answer

Step-by-step solution

Identify the components of the perimeter.

Calculate the total length of the straight sides.

Calculate the length of the curved side (semi-circle arc).

Calculate the total perimeter.

Try one yourself

Still stuck on this one?

More Mathematics Questions