Understanding geometric shape formulas is key in Pre-Algebra. These formulas help calculate areas, volumes, and perimeters of various shapes, making it easier to solve real-world problems. Mastering these concepts lays a strong foundation for future math studies.
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Area of a rectangle: A = length × width
- The area represents the total space inside the rectangle.
- Both the length and width must be in the same unit for accurate calculation.
- The formula can be applied to any rectangle, regardless of its dimensions.
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Area of a square: A = side²
- A square is a special type of rectangle where all sides are equal.
- The area is calculated by squaring the length of one side.
- This formula simplifies calculations for squares compared to rectangles.
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Area of a triangle: A = (base × height) ÷ 2
- The base can be any side of the triangle, and the height is the perpendicular distance from that base to the opposite vertex.
- This formula shows that the area of a triangle is half that of a rectangle with the same base and height.
- Understanding this formula is crucial for solving problems involving triangular shapes.
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Area of a circle: A = πr²
- The area is determined by the radius (r), which is the distance from the center to the edge of the circle.
- π (pi) is a constant approximately equal to 3.14, used to calculate circular areas.
- This formula is essential for problems involving circular objects or spaces.
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Circumference of a circle: C = 2πr
- The circumference is the total distance around the circle.
- It is directly related to the radius, making it easy to calculate if the radius is known.
- Understanding circumference is important for problems involving circular motion or boundaries.
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Volume of a rectangular prism: V = length × width × height
- Volume measures the space inside a three-dimensional object.
- All three dimensions (length, width, height) must be in the same unit for accurate results.
- This formula applies to any rectangular prism, including boxes and containers.
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Volume of a cube: V = side³
- A cube is a special case of a rectangular prism where all sides are equal.
- The volume is calculated by cubing the length of one side.
- This formula simplifies calculations for cubes compared to rectangular prisms.
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Perimeter of a rectangle: P = 2(length + width)
- The perimeter is the total distance around the rectangle.
- It is calculated by adding the lengths of all sides.
- This formula is useful for determining the boundary length of rectangular shapes.
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Perimeter of a square: P = 4 × side
- The perimeter of a square is simply four times the length of one side.
- This formula is straightforward due to the equal length of all sides.
- Understanding this helps in solving problems related to square shapes.
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Pythagorean theorem: a² + b² = c²
- This theorem applies to right triangles, relating the lengths of the sides.
- 'c' represents the hypotenuse, the longest side opposite the right angle.
- It is fundamental for solving problems involving right triangles and is widely used in geometry.