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Calculating the area of an object is a fundamental task in various fields, including mathematics, engineering, architecture, and geometry. It involves determining the amount of space enclosed within the boundaries of an object, whether it be a two-dimensional shape or a three-dimensional figure. This calculation is invaluable in numerous real-world scenarios, such as determining the amount of material needed for construction or estimating the space required for placing furniture in a room. By understanding the principles and formulas behind area calculation, individuals can accurately measure and manipulate space to solve practical problems efficiently. In this article, we will explore the concepts and methods involved in calculating the area of different objects, providing a comprehensive guide for anyone seeking to acquire this essential skill.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 18,311 times.
Finding the area of an object is easy only when you understand the techniques and formulas involved. If you master the knowledge, you can calculate the area and surface area of any object. Let’s start with Step 1.
Steps
Calculate the area of objects in the plane
- In this case, the object consists of the following shapes: triangle, trapezoid, rectangle, square, and semicircle.
- Area of Square = side 2 = a 2
- Area of Rectangle = width x height = wxh
- Area of Trapezoid = [(side 1 + side 2) x height]/2 = [(a + b) xh]/2
- Area of Triangle = base x height x 1/2 = (b + h)/2
- Area of Semicircle = (π x radius 2 )/2 = (π xr 2 )/2
- Square: a = 2.5 in
- Rectangle = w = 4.5 in, h = 2.5 in
- Trapezoid = a = 3 in, b = 5 in, h = 5 in
- Triangle = b = 3 in, h = 2.5 in
- Semicircle = r = 1.5 in
- Find the area of each figure:
- Area of square = 2.5 in 2 = 6.25 in 2
- Area of rectangle = 4.5 in x 2.5 in = 11.25 in 2
- Area of a trapezoid = [(3 in + 5 in) x 5 in]/2 = 20 in 2
- Area of triangle = 3 in x 2.5 in x 1/2 = 3.75 in 2
- Area of semicircle = 1.5 in 2 x x 1/2 = 3.53 in 2
- Add the areas of the shapes together:
- Area of object = Area of square + Area of rectangle + Area of trapezoid + Area of semicircle
- Area of object = 6.25 in 2 + 11.25 in 2 + 20 in 2 + 3.75 in 2 + 3.53 in 2
- Area of object = 44.78 in 2
Calculate the surface area of 3D objects
- Square surface area = 6 x side 2 = 6s 2
- Cone surface area = x radius x sides + x radius 2 = π xrxs + r 2
- Spherical surface area = 4 x x radius 2 = 4πr 2
- Cylindrical surface area = 2 x x radius 2 + 2 x π x radius x height = 2πr 2 + 2πrh
- Surface area of a pyramid with a square base = base 2 + 2 x base xh = b 2 + 2bh
- Cube = side = 3.5 in
- Cone = r = 2 in, h = 4 in
- Spherical = r = 3 in
- Cylinder = r = 2 in, h = 3.5 in
- A pyramid whose base is a square = b = 2 in, h = 4 in
- Surface area of cube = 6 x 3.5 2 = 73.5 in 2
- Cone Surface Area = (2 x 4) + x 2 2 = 37.7 in 2
- Spherical surface area = 4 x x 3 2 = 113.09 in 2
- Cylindrical surface area = 2π x 2 2 + 2π(2 x 3.5) = 69.1 in 2
- Surface area of a pyramid whose base is a square = 2 2 + 2(2 x 4) = 20 in 2
Advice
- Measure the dimensions of objects using a ruler or caliper
Warning
- Don’t confuse area and surface area, they are the same but are used differently. Area is used for in-plane objects and surface area is used in case of three-dimensional objects.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 18,311 times.
Finding the area of an object is easy only when you understand the techniques and formulas involved. If you master the knowledge, you can calculate the area and surface area of any object. Let’s start with Step 1.
In conclusion, calculating the area of an object is a fundamental concept in geometry and is applicable to various real-life situations. By knowing the formula and method to determine the area, one can accurately measure the space occupied by an object. Whether it is a simple geometric shape or a complex irregular figure, the process of calculating area involves breaking down the object into smaller components and summing their areas. Additionally, the use of modern technology, such as software and image-processing tools, has made it even easier to measure the area of objects accurately. Understanding how to calculate the area not only helps in academic or professional settings but also in everyday situations, such as determining how much paint or flooring material is required for a room. Overall, mastering the skill of calculating the area of an object is essential for a deeper understanding of geometry and practical applications in various fields.
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