A Company Designs A Logo Using A Kite Figure Around The Letter $t$.The Logo Is 12 Centimeters Wide And 16 Centimeters Tall. What Is The Area Of The Logo?A. 48 Sq. Cm B. 96 Sq. Cm C. 144 Sq. Cm D. 192 Sq. Cm
Introduction
In this problem, we are tasked with finding the area of a logo designed by a company using a kite figure around the letter "t". The logo has a width of 12 centimeters and a height of 16 centimeters. To solve this problem, 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 lines that make up the letter. The width of the kite is 12 centimeters, and the height is 16 centimeters.
Calculating the Area of a Kite
To calculate the area of a kite, we need to use the formula:
Area = (d1 × d2) / 2
where d1 and d2 are the lengths of the diagonals of the kite.
Finding the Diagonals of the Kite
The diagonals of the kite are the lines that connect the opposite vertices of the kite. In this case, the diagonals are the vertical and horizontal lines that make up the letter "t". The length of the vertical diagonal is equal to the height of the kite, which is 16 centimeters. The length of the horizontal diagonal is equal to the width of the kite, which is 12 centimeters.
Calculating the Area
Now that we have the lengths of the diagonals, we can plug them into the formula to calculate the area of the kite:
Area = (16 × 12) / 2 Area = 192 / 2 Area = 96
Conclusion
Therefore, the area of the logo is 96 square centimeters.
Answer
The correct answer is B. 96 sq. cm.
Additional Information
It's worth noting that the area of the logo can also be calculated using the formula for the area of a rectangle, which is:
Area = length × width
In this case, the length of the rectangle is 16 centimeters, and the width is 12 centimeters. Plugging these values into the formula, we get:
Area = 16 × 12 Area = 192
However, this is the area of the entire rectangle, not just the kite figure. To find the area of the kite, we need to divide the area of the rectangle by 2, since the kite is formed by two triangles that make up half of the rectangle. Therefore, the area of the kite is:
Area = 192 / 2 Area = 96
Final Thoughts
Introduction
In our previous article, we discussed how to calculate the area of a logo designed by a company using a kite figure around the letter "t". The logo has a width of 12 centimeters and a height of 16 centimeters. In this article, we will answer some frequently asked questions related to the problem.
Q: What is the formula for calculating the area of a kite?
A: The formula for calculating 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 diagonals of the kite?
A: The diagonals of the kite are the lines that connect the opposite vertices of the kite. In this case, the diagonals are the vertical and horizontal lines that make up the letter "t". The length of the vertical diagonal is equal to the height of the kite, which is 16 centimeters. The length of the horizontal diagonal is equal to the width of the kite, which is 12 centimeters.
Q: Can I use the formula for the area of a rectangle to calculate the area of the kite?
A: Yes, you can use the formula for the area of a rectangle to calculate the area of the kite. The area of the rectangle is:
Area = length × width
In this case, the length of the rectangle is 16 centimeters, and the width is 12 centimeters. Plugging these values into the formula, we get:
Area = 16 × 12 Area = 192
However, this is the area of the entire rectangle, not just the kite figure. To find the area of the kite, we need to divide the area of the rectangle by 2, since the kite is formed by two triangles that make up half of the rectangle. Therefore, the area of the kite is:
Area = 192 / 2 Area = 96
Q: Why do I need to divide the area of the rectangle by 2 to find the area of the kite?
A: You need to divide the area of the rectangle by 2 to find the area of the kite because the kite is formed by two triangles that make up half of the rectangle. By dividing the area of the rectangle by 2, you are essentially finding the area of one of the triangles that make up the kite.
Q: Can I use any other method to calculate the area of the kite?
A: Yes, you can use any other method to calculate the area of the kite as long as it is a valid method. Some other methods include using the formula for the area of a triangle or using the formula for the area of a parallelogram.
Q: What is the area of the logo in square centimeters?
A: The area of the logo is 96 square centimeters.
Conclusion
In conclusion, the area of the logo is 96 square centimeters. This problem requires a basic understanding of geometry and the properties of a kite. By using the formula for the area of a kite, we can calculate the area of the logo and determine the correct answer.
Additional Resources
If you are interested in learning more about geometry and the properties of a kite, we recommend checking out the following resources:
We hope this article has been helpful in answering your questions about the problem. If you have any further questions, please don't hesitate to ask.