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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.
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