Finding the Area of the Shaded Part

Oct 13, 2025 by windailys.com 55 views

Introduction

In geometry, finding the areas of shaded parts in figures is a crucial concept that helps us understand the spatial relationships between different shapes and objects. The shaded areas can be triangles, trapezoids, or any other type of polygon. In this article, we will explore how to find the areas of shaded parts in geometric figures using various techniques and formulas.

Understanding the Figures

Before we dive into finding the areas of shaded parts, let's take a closer look at the figures provided:

(i) 22 m 8m 38 m 20m

This figure consists of two rectangles, one with dimensions 22m x 8m and the other with dimensions 38m x 20m. The shaded area is the region between these two rectangles.

Finding the Area of the Shaded Part

To find the area of the shaded part, we need to find the area of the larger rectangle and subtract the area of the smaller rectangle.

Step 1: Find the Area of the Larger Rectangle

The area of a rectangle is given by the formula:

Area = length x width

In this case, the length of the larger rectangle is 38m and the width is 20m. Therefore, the area of the larger rectangle is:

Area = 38m x 20m = 760m²

Step 2: Find the Area of the Smaller Rectangle

The area of the smaller rectangle is given by the formula:

Area = length x width

In this case, the length of the smaller rectangle is 22m and the width is 8m. Therefore, the area of the smaller rectangle is:

Area = 22m x 8m = 176m²

Step 3: Find the Area of the Shaded Part

Now that we have the areas of both rectangles, we can find the area of the shaded part by subtracting the area of the smaller rectangle from the area of the larger rectangle:

Area of shaded part = Area of larger rectangle - Area of smaller rectangle = 760m² - 176m² = 584m²

Conclusion

In this article, we learned how to find the areas of shaded parts in geometric figures using the formula for the area of a rectangle. We applied this formula to a figure consisting of two rectangles and found the area of the shaded part to be 584m². This technique can be applied to various types of figures and shapes to find the areas of shaded parts.

Real-World Applications

Finding the areas of shaded parts in geometric figures has numerous real-world applications, such as:

Architecture: Architects use geometric figures to design buildings and structures. Finding the areas of shaded parts helps them determine the amount of materials needed for construction.
Engineering: Engineers use geometric figures to design machines and mechanisms. Finding the areas of shaded parts helps them determine the amount of energy required to operate the machine.
Land Surveying: Land surveyors use geometric figures to measure the area of land. Finding the areas of shaded parts helps them determine the amount of land that is not usable.

Tips and Tricks

Here are some tips and tricks to help you find the areas of shaded parts in geometric figures:

Use the formula for the area of a rectangle: The formula for the area of a rectangle is length x width. Make sure to use this formula to find the area of each rectangle.
Subtract the areas: To find the area of the shaded part, subtract the area of the smaller rectangle from the area of the larger rectangle.
Use a calculator: If you are dealing with large numbers, use a calculator to find the area of each rectangle and the shaded part.

Practice Problems

Here are some practice problems to help you practice finding the areas of shaded parts in geometric figures:

Problem 1: Find the area of the shaded part in the figure below:


10m	20m	30m
5m	15m	25m

Problem 2: Find the area of the shaded part in the figure below:


20m	30m	40m
10m	20m	30m

Conclusion

Finding the areas of shaded parts in geometric figures is a crucial concept that helps us understand the spatial relationships between different shapes and objects. By using the formula for the area of a rectangle and subtracting the areas, we can find the area of the shaded part. This technique has numerous real-world applications and can be applied to various types of figures and shapes.

Introduction

In our previous article, we discussed how to find the areas of shaded parts in geometric figures using the formula for the area of a rectangle. However, we understand that you may still have some questions about this topic. In this article, we will address some of the most frequently asked questions (FAQs) about finding the areas of shaded parts in geometric figures.

Q: What is the formula for finding the area of a shaded part?

A: The formula for finding the area of a shaded part is:

Area of shaded part = Area of larger rectangle - Area of smaller rectangle

Q: How do I find the area of a rectangle?

A: To find the area of a rectangle, you need to multiply the length and width of the rectangle. The formula for the area of a rectangle is:

Area = length x width

Q: What if the shaded part is not a rectangle?

A: If the shaded part is not a rectangle, you will need to use a different formula to find its area. For example, if the shaded part is a triangle, you will need to use the formula for the area of a triangle:

Area = (base x height) / 2

Q: Can I use a calculator to find the area of a shaded part?

A: Yes, you can use a calculator to find the area of a shaded part. In fact, using a calculator can save you time and reduce the risk of errors.

Q: How do I determine which rectangle is the larger rectangle?

A: To determine which rectangle is the larger rectangle, you need to compare the lengths and widths of the two rectangles. The rectangle with the longer length and/or wider width is the larger rectangle.

Q: What if the shaded part is not a simple shape?

A: If the shaded part is not a simple shape, you may need to break it down into smaller shapes and find the area of each shape separately. For example, if the shaded part is a combination of two triangles and a rectangle, you will need to find the area of each shape separately and then add them together.

Q: Can I use this method to find the area of a shaded part in a 3D figure?

A: No, this method is only applicable to 2D figures. If you need to find the area of a shaded part in a 3D figure, you will need to use a different method, such as finding the surface area of the figure.

Q: How do I know if the shaded part is a rectangle or not?

A: To determine if the shaded part is a rectangle or not, you need to check if it has four right angles and opposite sides of equal length. If it does, then it is a rectangle.

Q: Can I use this method to find the area of a shaded part in a figure with multiple rectangles?

A: Yes, you can use this method to find the area of a shaded part in a figure with multiple rectangles. Simply find the area of each rectangle separately and then subtract the areas of the rectangles that are not part of the shaded area.

Conclusion

We hope that this article has helped to answer some of the most frequently asked questions (FAQs) about finding the areas of shaded parts in geometric figures. Remember to always use the formula for the area of a rectangle and to subtract the areas of the rectangles that are not part of the shaded area. If you have any further questions, please don't hesitate to ask.

Practice Problems

Here are some practice problems to help you practice finding the areas of shaded parts in geometric figures:

Problem 1: Find the area of the shaded part in the figure below:


10m	20m	30m
5m	15m	25m

Problem 2: Find the area of the shaded part in the figure below:


20m	30m	40m
10m	20m	30m

Real-World Applications

Finding the areas of shaded parts in geometric figures has numerous real-world applications, such as:

Architecture: Architects use geometric figures to design buildings and structures. Finding the areas of shaded parts helps them determine the amount of materials needed for construction.
Engineering: Engineers use geometric figures to design machines and mechanisms. Finding the areas of shaded parts helps them determine the amount of energy required to operate the machine.
Land Surveying: Land surveyors use geometric figures to measure the area of land. Finding the areas of shaded parts helps them determine the amount of land that is not usable.

Tips and Tricks

Here are some tips and tricks to help you find the areas of shaded parts in geometric figures:

Use the formula for the area of a rectangle: The formula for the area of a rectangle is length x width. Make sure to use this formula to find the area of each rectangle.
Subtract the areas: To find the area of the shaded part, subtract the area of the smaller rectangle from the area of the larger rectangle.
Use a calculator: If you are dealing with large numbers, use a calculator to find the area of each rectangle and the shaded part.