How to Calculate the Area of an Object

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.

Table of Contents

Calculate the area of objects in the plane

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Determine the shape of the object. If your object has an unidentifiable shape such as a circle or a trapezoid, which can be made up of many different shapes, you must know what these are in order to separate larger objects into larger objects. smaller body.

In this case, the object consists of the following shapes: triangle, trapezoid, rectangle, square, and semicircle.

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Write down the formula for the area of each figure. These formulas will allow you to use the given measurements of each shape to find their area. Here is the formula to find the area of each shape:

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

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Write down the dimensions of each shape. Once you have the formula, write down the dimensions of each shape so you can substitute those values into the formula. Here are the dimensions of each figure:

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

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Use the formula and dimensions given to calculate the area of each shape and add them together. Finding the area of each shape will help you find the area of each part of the object; Once you have found the area of each shape using the given formula and measurements, all you have to do is add the areas together to find the area of the whole object. When calculating the area, you must keep in mind that the area is in square units. The area of the entire object is 44.78 in ² . Here’s how to do it:

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

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Write down the formula for calculating the surface area of each shape. Surface area is the total area of an object’s faces and curved surfaces. All three-dimensional objects have a surface area; volume is the amount of space occupied by the object. Here is the formula for calculating the surface area of various 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

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Write down the dimensions of each shape. Their sizes are as follows:

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

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Calculate the surface area of each figure. Now, all you need to do is plug the respective dimensions of each shape into the formula for the surface area of each shape and that’s it. Here’s how to do it:

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.

Steps

Calculate the area of objects in the plane

Calculate the surface area of 3D objects

Advice

Warning

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