Finding the area of an object is very easy as long as you understand the techniques and formulas used. If you have the right knowledge, you can find the area and surface area of any object. See Step 1 below to get started.
Step
Method 1 of 2: Calculating the Area of a Two-Dimensional Object
Step 1. Identify the shape of the object
If your object is not an easily identifiable shape, such as a circle or a trapezoid, then your object may be made up of several shapes. You have to know the shapes that make up the big building.
In this problem, the object consists of several shapes: a triangle, a trapezoid, a square, a quadrilateral, and a semicircle
Step 2. Write down the formulas to find the area of each figure
These formulas will allow you to use the known measurements of each shape to find its area. Here are the formulas for finding the area of each shape:
- Area of Square = side2 = a2
- Area of the rectangle = width x height = l x t
- Area of the Trapezoid = [(side 1 + side 2) x height]/2 = [(a + b) x h]/2
- Area of Triangle = base x height x 1/2 = (a + t)/2
- Area of Semicircle = (π x radius2)/2 = (π x r2)/2
Step 3. Write down the dimensions of each shape
After you write down the formulas, write down the dimensions of each formula so you can enter the values. Here are the dimensions of each build:
- Square: a = 2.5 cm
- Square = l = 4.5 cm, t = 2.5 cm
- Trapezoid = a = 3 cm, b = 5 cm, t = 5 cm
- Triangle = a = 3 cm, t = 2.5 cm
- Semicircle = r = 1.5 cm
Step 4. Use formulas and dimensions to find the area of each object and add them up
By finding the area of each shape, you can find the area of the building that composes it; After you know the area of each building using the formula and measurements given, all you have to do to find the area of the entire building is add them up. When calculating the area, you must remember to write the area in square units. The total area of the building is 44.78 cm2. Here's how to calculate it:
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Find the area of each shape:
- Square Area = 2.5 cm2 = 6.25 cm2
- Square = 4.5 cm x 2.5 cm = 11.25 cm2
- Trapezoid = [(3 cm + 5 cm) x 5 cm]/2 = 20 cm2
- Triangle = 3 cm x 2.5 cm x 1/2 = 3.75 cm2
- Half Circle = 1.5 cm2 x x 1/2 = 3.53 cm2
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Add up the area of each shape:
- Area of object = area of square + area of quad + area of trapezoid + area of triangle + area of semi circle
- Area of Object = 6.25 cm2 + 11.25 cm2 + 20 cm2 + 3.75 cm2 + 3.53 cm2
- Area of Object = 44, 78 cm2
Method 2 of 2: Calculating the Surface Area of 3-D Objects
Step 1. Write down the formulas to find the surface area of each shape
Surface area is the total area of the surface of any object. Every three-dimensional object has a surface area; its volume is the amount of space occupied by the object. Here are the formulas for finding the surface area of various objects:
- Surface area of a cube = 6 x sides2 = 6s2
- Cone surface area = x radius x side + x radius2 = x r x s + r2
- Surface area of the sphere = 4 x x radius2 = 4πr2
- Surface area of the cylinder = 2 x x radius2 + 2 x x radius x height = 2πr2 + 2πrt
- Surface area of a square pyramid = side of the base2 + 2 x side of base x t = s2 + 2st
Step 2. Write down the dimensions of each shape
Here are the dimensions:
- Cube = side = 3.5 cm
- Cone = r = 2 cm, t = 4 cm
- Ball = r = 3 cm
- Tube = r = 2 cm, t = 3.5 cm
- Square Pyramid = s = 2 cm, t = 4 cm
Step 3. Calculate the surface area of each shape
Now, all you have to do is plug the dimensions of each shape into the formula to find the surface area of each shape and you're done. Here's how:
- Surface area of a cube = 6 x 3, 52 = 73.5 cm2
- Surface area of cone = (2 x 4) + x 22 = 37.7 cm2
- Surface area of the sphere = 4 x x 32 = 113, 09 cm2
- Surface area of the cylinder = 2π x 22 + 2π(2 x 3, 5) = 69, 1 cm2
- Surface area of a square pyramid = 22 + 2(2 x 4) = 20 cm2
