list of all geometry formulas pdf
2D Geometry Formulas
Download a PDF with essential formulas for 2D shapes. Includes squares, rectangles, triangles, circles, parallelograms, trapezoids, sectors, and regular polygons. Covers perimeters, areas, and key properties for each shape. Perfect for quick reference and problem-solving.
- Square: Perimeter = 4s, Area = s²
- Rectangle: Perimeter = 2(l + w), Area = l × w
- Triangle: Perimeter = a + b + c, Area = (1/2) × base × height
- Circle: Circumference = 2πr, Area = πr²
- Parallelogram: Perimeter = 2(a + b), Area = base × height
- Trapezoid: Perimeter = a + b + c + d, Area = (1/2) × (a + b) × height
- Sector: Area = (1/2) × r² × θ, Arc Length = r × θ
- Regular Polygon: Perimeter = n × s, Area = (1/2) × n × s × a
Get the PDF for easy access to all 2D geometry formulas. Ideal for students and educators.
Rectangle Formulas
Rectangles are four-sided shapes with opposite sides equal and all angles at 90 degrees. The key formulas for rectangles are:
- Perimeter of a Rectangle: The total distance around the rectangle;
Formula: P = 2 × (length + width) - Area of a Rectangle: The space inside the rectangle.
Formula: A = length × width
These formulas are essential for solving problems involving rectangles. The perimeter helps in calculating the boundary, while the area measures the space inside. For example, if a rectangle has a length of 5 units and a width of 3 units:
- Perimeter = 2 × (5 + 3) = 16 units
- Area = 5 × 3 = 15 square units
These formulas are widely used in geometry and real-world applications. They can be found in geometry formulas PDF documents for quick reference. Perfect for students and educators to solve problems efficiently.
Triangle Formulas
Triangles are three-sided polygons with three vertices and three angles. Key formulas for triangles include:
- Perimeter of a Triangle: The sum of all three sides.
Formula: P = a + b + c - Area of a Triangle: The space inside the triangle.
Formula: A = (1/2) × base × height - Pythagorean Theorem: For right-angled triangles, relating the sides.
Formula: a² + b² = c² (where c is the hypotenuse) - Heron’s Formula: Calculates the area when all three sides are known.
Formula: A = √[s(s ー a)(s ⎻ b)(s ー c)] (where s = (a + b + c) / 2)
These formulas are fundamental for solving problems involving triangles. For example, if a triangle has sides of 3, 4, and 5 units:
- Perimeter = 3 + 4 + 5 = 12 units
- Area = (1/2) × 4 × 3 = 6 square units
Find these and more triangle formulas in a geometry formulas PDF for easy access. Essential for students and educators to tackle geometric problems efficiently.
Circle Formulas
Circles are round shapes with all points equidistant from the center. Essential formulas for circles include:
- Circumference: The distance around the circle.
Formula: C = 2πr or C = πd (where d = diameter) - Area: The space inside the circle.
Formula: A = πr² - Diameter: The distance across the circle through the center.
Formula: d = 2r - Sector Area: The area of a portion of the circle.
Formula: A = (1/2) × r² × θ (where θ is the central angle in radians) - Arc Length: The length of a portion of the circumference.
Formula: L = r × θ
For example, if a circle has a radius of 5 units:
- Circumference = 2 × π × 5 = 10π units
- Area = π × 5² = 25π square units
These formulas are crucial for solving problems involving circles. Find them and more in a geometry formulas PDF for easy access and reference.
Parallelogram Formulas
A parallelogram is a four-sided shape with opposite sides equal and parallel. Key formulas for parallelograms include:
- Perimeter: The total distance around the shape.
Formula: P = 2(a + b) (where a and b are the lengths of adjacent sides) - Area: The space inside the parallelogram.
Formula: A = base × height (height is the perpendicular distance between the base and its opposite side)
For example, if a parallelogram has sides of 6 and 4 units, and a height of 3 units:
- Perimeter = 2(6 + 4) = 20 units
- Area = 6 × 3 = 18 square units
These formulas are essential for calculating the perimeter and area of parallelograms. They are widely used in geometry and can be found in a geometry formulas PDF for quick reference and study.
Trapezoid Formulas
A trapezoid is a quadrilateral with at least one pair of parallel sides, known as the bases. The formulas for trapezoids are fundamental for calculating their perimeter and area.
- Perimeter: The sum of all sides.
Formula: P = a + b + c + d (where a, b, c, d are the lengths of the sides) - Area: The space inside the trapezoid.
Formula: A = (1/2) × (a + b) × h (where a and b are the lengths of the two bases, and h is the height)
For example, if a trapezoid has bases of 5 and 7 units, and a height of 4 units:
- Area = (1/2) × (5 + 7) × 4 = 24 square units
These formulas are essential for solving problems involving trapezoids. They are commonly included in geometry formulas PDF guides for easy access and reference.
Sector of a Circle Formulas
A sector of a circle is a portion bounded by two radii and an arc. Its formulas help calculate the area and arc length.
- Arc Length: The length of the curved edge.
Formula: s = rθ (where r is the radius and θ is the central angle in radians) - Area: The space inside the sector.
Formula: A = (1/2) × r² × θ
For example, if a sector has a radius of 8 units and a central angle of 2 radians:
- Arc Length = 8 × 2 = 16 units
- Area = (1/2) × 8² × 2 = 64 square units
These formulas are essential for solving problems involving sectors; They are commonly included in geometry formulas PDF guides for easy access and reference.
3D Geometry Formulas
Explore formulas for calculating volumes and surface areas of 3D shapes like prisms, pyramids, and more. Download a PDF for quick access to formulas for cubes, cylinders, cones, and other solids. Essential for solving 3D geometry problems.
- Rectangular Prism: Volume = lwh, Surface Area = 2(lw + lh + wh)
- Square Pyramid: Volume = (1/3) × base × height, Surface Area = base + (4 × triangular faces)
- Cylinder: Volume = πr²h, Surface Area = 2πr(r + h)
These formulas are crucial for understanding and solving 3D geometry problems. They are often included in geometry formulas PDF guides for easy reference and study.
Prism Formulas
A prism is a 3D shape with two identical ends and flat faces. Its volume and surface area can be calculated using specific formulas.
- Volume of a Prism:
The volume ( V ) of a prism is given by:
[ V = ext{Base Area} imes ext{Height} ]
For a rectangular prism, this becomes:
[ V = l imes w imes h ]
where ( l ), ( w ), and ( h ) are length, width, and height. - Surface Area of a Prism:
The total surface area ( A ) of a prism is the sum of the lateral surface area and the areas of the two bases:[ A = 2 imes ext{Base Area} + ext{Lateral Surface Area} ]
For a rectangular prism:
[ A = 2(lw + lh + wh) ]
These formulas are essential for calculating the volume and surface area of prisms. They are commonly included in geometry formulas PDF guides for easy reference and study.
Pyramid Formulas
A pyramid is a 3D shape with a base and triangular faces that meet at a common point (apex). The volume and surface area of pyramids are calculated using specific formulas.
- Volume of a Pyramid:
The volume ( V ) of a pyramid is given by:
[ V = rac{1}{3} imes ext{Base Area} imes ext{Height} ]
For a square pyramid with base side length ( s ) and height ( h ):
[ V = rac{1}{3}s^2h ]
The total surface area ( A ) includes the base area and the lateral surface area:
[ A = ext{Base Area} + rac{1}{2} imes ext{Perimeter of Base} imes ext{Slant Height} ]
For a square pyramid:
[ A = s^2 + 4 imes rac{1}{2}s l ]
where ( l ) is the slant height.
These formulas are essential for calculating the volume and surface area of pyramids and are included in most geometry formulas PDF guides for reference.
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