Calculating the Area of the Logo

Oct 13, 2025 by vinooalluri.com 18 views

Introduction

In this problem, we are tasked with finding the area of a logo designed using a kite figure around the letter "t". The logo has a width of 12 centimeters and a height of 16 centimeters. To find the area of the logo, we need to understand the properties of a kite and how to calculate its area.

Properties of a Kite

A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the kite figure is formed around the letter "t", with the two pairs of adjacent sides being the vertical and horizontal sides of the kite. The area of a kite can be calculated using the formula:

Area = (d1 × d2) / 2

where d1 and d2 are the lengths of the diagonals of the kite.

Calculating the Area of the Logo

To calculate the area of the logo, we need to find the lengths of the diagonals of the kite. Since the logo is 12 centimeters wide and 16 centimeters tall, we can use the Pythagorean theorem to find the lengths of the diagonals.

Let's call the width of the logo "w" and the height of the logo "h". We can use the Pythagorean theorem to find the length of the diagonal that runs from the top left corner of the kite to the bottom right corner:

d1 = √(w^2 + h^2) d1 = √(12^2 + 16^2) d1 = √(144 + 256) d1 = √400 d1 = 20

Now, let's find the length of the diagonal that runs from the top right corner of the kite to the bottom left corner:

d2 = √(w^2 + h^2) d2 = √(12^2 + 16^2) d2 = √(144 + 256) d2 = √400 d2 = 20

Since the two diagonals are equal in length, we can use the formula for the area of a kite:

Area = (d1 × d2) / 2 Area = (20 × 20) / 2 Area = 400 / 2 Area = 200

However, this is not the correct answer. We need to consider the fact that the kite figure is formed around the letter "t", which means that the logo has a smaller area than the area of the rectangle formed by the width and height of the logo.

To find the correct area of the logo, we need to subtract the area of the two triangles that are not part of the kite figure from the area of the rectangle.

Calculating the Area of the Two Triangles

The two triangles that are not part of the kite figure are right triangles with a base of 6 centimeters and a height of 8 centimeters. We can use the formula for the area of a triangle:

Area = (base × height) / 2 Area = (6 × 8) / 2 Area = 48 / 2 Area = 24

Since there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the two triangles:

Total Area of Triangles = 2 × 24 Total Area of Triangles = 48

Finding the Correct Area of the Logo

Now that we have the area of the two triangles, we can subtract this area from the area of the rectangle to find the correct area of the logo:

Area of Rectangle = w × h Area of Rectangle = 12 × 16 Area of Rectangle = 192

Area of Logo = Area of Rectangle - Total Area of Triangles Area of Logo = 192 - 48 Area of Logo = 144

Therefore, the correct answer is C. 144 sq. cm.

Conclusion

Introduction

In our previous article, we explored the problem of finding the area of a logo designed using a kite figure around the letter "t". We used the properties of a kite and the Pythagorean theorem to find the lengths of the diagonals of the kite, and then used the formula for the area of a kite to calculate the area of the logo. However, we needed to consider the fact that the kite figure is formed around the letter "t", which means that the logo has a smaller area than the area of the rectangle formed by the width and height of the logo.

In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the problem.

Q&A Section

Q: What is the formula for the area of a kite?

A: The formula for the area of a kite is:

Area = (d1 × d2) / 2

where d1 and d2 are the lengths of the diagonals of the kite.

Q: How do I find the lengths of the diagonals of the kite?

A: To find the lengths of the diagonals of the kite, you can use the Pythagorean theorem. Let's call the width of the logo "w" and the height of the logo "h". We can use the Pythagorean theorem to find the length of the diagonal that runs from the top left corner of the kite to the bottom right corner:

d1 = √(w^2 + h^2)

Now, let's find the length of the diagonal that runs from the top right corner of the kite to the bottom left corner:

d2 = √(w^2 + h^2)

Since the two diagonals are equal in length, we can use the formula for the area of a kite.

Q: Why do I need to subtract the area of the two triangles that are not part of the kite figure from the area of the rectangle?

A: The kite figure is formed around the letter "t", which means that the logo has a smaller area than the area of the rectangle formed by the width and height of the logo. The two triangles that are not part of the kite figure are right triangles with a base of 6 centimeters and a height of 8 centimeters. We need to subtract the area of these two triangles from the area of the rectangle to find the correct area of the logo.

Q: How do I calculate the area of the two triangles that are not part of the kite figure?

A: To calculate the area of the two triangles, we can use the formula for the area of a triangle:

Area = (base × height) / 2

Since there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the two triangles.

Q: What is the correct answer to the problem?

A: The correct answer to the problem is C. 144 sq. cm.

Conclusion

In this article, we provided a Q&A section to help clarify any doubts and provide additional information on the problem of finding the area of a logo designed using a kite figure around the letter "t". We hope that this article has been helpful in understanding the problem and its solution.

Additional Resources

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[How to Calculate the Area of a Rectangle](link to article)
[How to Calculate the Area of a Triangle](link to article)
[How to Use the Pythagorean Theorem](link to article)

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