In this section, we will learn how to calculate the perimeter, area, volumes, and angles of basic geometric shapes. Understanding these concepts is fundamental in geometry and will help you solve various mathematical problems.
The perimeter is the distance around a two-dimensional shape.
The perimeter (P) of a rectangle is calculated using the formula:
\[P = 2(l + w)\]where (l) is the length and (w) is the width.
The perimeter (P) of a triangle is the sum of the lengths of its sides:
\[P = a + b + c\]where (a), (b), and (c) are the lengths of the sides.
The perimeter (circumference) (C) of a circle is calculated using the formula:
\[C = 2\pi r\]where (r) is the radius.
The area is the amount of space inside a two-dimensional shape.
The area (A) of a rectangle is calculated using the formula:
\[A = l \times w\]where (l) is the length and (w) is the width.
The area (A) of a triangle is calculated using the formula:
\[A = \frac{1}{2} \times b \times h\]where (b) is the base and (h) is the height.
The area (A) of a circle is calculated using the formula:
\[A = \pi r^2\]where (r) is the radius.
The volume is the amount of space inside a three-dimensional shape.
The volume (V) of a cube is calculated using the formula:
\[V = s^3\]where (s) is the length of a side.
The volume (V) of a rectangular prism is calculated using the formula:
\[V = l \times w \times h\]where (l) is the length, (w) is the width, and (h) is the height.
The volume (V) of a cylinder is calculated using the formula:
\[V = \pi r^2 h\]where (r) is the radius and (h) is the height.
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