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- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/02%3A_Geometry/2.02%3A_Perimeter_Circumference_and_AreaQuadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understan...Quadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understanding the properties of different quadrilaterals can help you in solving problems that involve this type of polygon.
- https://math.libretexts.org/Courses/College_of_the_Canyons/Math_130%3A_Math_for_Elementary_School_Teachers_(Lagusker)/06%3A_Geometry/6.03%3A_Area_Surface_Area_and_VolumeThink inside the box and approximate the Shaded Area: (area of a square is base times height) Think around the box (surface area) and approximate the Shaded Area: (How many sides are not seen in the p...Think inside the box and approximate the Shaded Area: (area of a square is base times height) Think around the box (surface area) and approximate the Shaded Area: (How many sides are not seen in the picture, which must be included in the final answer?) Think inside the box (volume) and approximate the Shaded Area: Volume is base time’s height times width. Explain the difference between area, surface area, and volume. Find the Surface Area of the following shapes:
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/06%3A_Geometry/6.02%3A_Perimeter_Circumference_and_AreaQuadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understan...Quadrilaterals are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understanding the properties of different quadrilaterals can help you in solving problems that involve this type of polygon.
- https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/09%3A_Geometry/9.03%3A_Perimeter_and_AreaA long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as th...A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse. If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.03%3A_Trigonometric_Substitution/3.3E%3A_Exercises_for_Section_3.3This page presents mathematical exercises focused on simplifying trigonometric and hyperbolic expressions, completing the square for trinomials, and performing integrals using trigonometric substituti...This page presents mathematical exercises focused on simplifying trigonometric and hyperbolic expressions, completing the square for trinomials, and performing integrals using trigonometric substitution. It includes notable results like simplifying 9sec2θ−9 to 9tan2θ and evaluating various integrals.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.01%3A_Approximating_Areas/1.1E%3A_Exercises_for_Section_1.1This page presents a comprehensive overview of mathematical concepts, focusing on Riemann sums for estimating areas under curves through left and right endpoint approximations. It connects these calcu...This page presents a comprehensive overview of mathematical concepts, focusing on Riemann sums for estimating areas under curves through left and right endpoint approximations. It connects these calculations to real-world scenarios, such as tracking ride times and cumulative increases in environmental factors.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/03%3A_Vector_Calculus/3.04%3A_Greens_TheoremGreen’s theorem is an extension of the Fundamental Theorem of Calculus to two dimensions. It has two forms: a circulation form and a flux form, both of which require region D in the double integra...Green’s theorem is an extension of the Fundamental Theorem of Calculus to two dimensions. It has two forms: a circulation form and a flux form, both of which require region D in the double integral to be simply connected. However, we will extend Green’s theorem to regions that are not simply connected. Green’s theorem relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/02%3A_Multiple_Integration/2.03%3A_Double_Integrals_in_Polar_Coordinates/2.3E%3A_ExercisesThis page offers a collection of exercises and solutions focused on evaluating double integrals using polar coordinates. It covers conversions from rectangular to polar coordinates, area and volume ca...This page offers a collection of exercises and solutions focused on evaluating double integrals using polar coordinates. It covers conversions from rectangular to polar coordinates, area and volume calculations under various geometric shapes (like cones and spheres), and the properties of radial functions. Key topics include evaluating integrals, calculating areas and volumes, and understanding joint density functions associated with normal distributions.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/02%3A_Multiple_Integration/2.02%3A_Double_Integrals_over_General_Regions/2.2E%3A_ExercisesThis page covers the classification of regions in calculus as Type I and Type II for integral evaluations, detailing calculations for areas and volumes under specified functions. It includes practical...This page covers the classification of regions in calculus as Type I and Type II for integral evaluations, detailing calculations for areas and volumes under specified functions. It includes practical exercises on double integrals and explores geometric interpretations in three-dimensional space. Additionally, it discusses the lunes of Alhazen, proving their area is equivalent to that of a corresponding triangle.
- https://math.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/College_Technical_Math_1A_(NWTC)/07%3A_Geometry/7.02%3A_Area_of_Polygons_and_CirclesWe have seen that the perimeter of a polygon is the distance around the outside. Perimeter is a length, which is one-dimensional, and so it is measured in linear units (feet, centimeters, miles, etc.)...We have seen that the perimeter of a polygon is the distance around the outside. Perimeter is a length, which is one-dimensional, and so it is measured in linear units (feet, centimeters, miles, etc.). The area of a polygon is the amount of two-dimensional space inside the polygon, and it is measured in square units: square feet, square centimeters, square miles, etc.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/04%3A_Determinants/4.03%3A_Determinants_and_VolumesThis page explores the connections between matrices, their determinants, and geometric volumes, focusing on parallelepipeds. It defines parallelepipeds and illustrates how the determinant relates to t...This page explores the connections between matrices, their determinants, and geometric volumes, focusing on parallelepipeds. It defines parallelepipeds and illustrates how the determinant relates to their volume, covering key determinant properties and their impact on area and volume calculations for parallelograms and triangles. The text demonstrates how linear transformations scale volumes by the absolute value of the determinant.
