Calculate the perimeter of the following shapes
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
c) The shape is a triangle with side lengths $3 \text{ cm}$, $4 \text{ cm}$, and $5 \text{ cm}$.
Step 1: Identify the formula for the perimeter of a triangle.
The perimeter $P$ of a triangle with side lengths $a$, $b$, and $c$ is given by:
$$P = a+b+c$$
Step 2: Substitute the given side lengths into the formula.
$$P = 3 \text{ cm} + 4 \text{ cm} + 5 \text{ cm}$$
Step 3: Calculate the perimeter.
$$P = 12 \text{ cm}$$
The perimeter of the triangle is $\boxed{\text{12 cm}}$.
d) The shape is a circle with a radius of $3 \text{ cm}$.
Step 1: Identify the formula for the perimeter (circumference) of a circle.
The circumference $C$ of a circle with radius $r$ is given by:
$$C = 2\pi r$$
Step 2: Substitute the given radius into the formula.
$$C = 2 \times \pi \times 3 \text{ cm}$$
Step 3: Calculate the circumference.
$$C = 6\pi \text{ cm}$$
Using $\pi \approx 3.14159$:
$$C \approx 6 \times 3.14159 \text{ cm}$$
$$C \approx 18.85 \text{ cm}$$
The perimeter (circumference) of the circle is $\boxed{\text{6\pi cm}}$ or approximately $\boxed{\text{18.85 cm}}$.
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