6. ABCD Is A Parallelogram, DL And BM Are Heights On AB And AD Respectively . If The Area Of The Parallelogram Is 1470 Sq Cm, AB=35 Cm And AD = 49 Cm, Find The Length Of BM And DL.

Mar 1, 2025 by ADMIN 182 views

**Solving for BM and DL in a Parallelogram**

Understanding the Problem

In this problem, we are given a parallelogram ABCD with heights DL and BM on AB and AD respectively. We are also given the area of the parallelogram, which is 1470 sq cm, and the lengths of AB and AD, which are 35 cm and 49 cm respectively. Our goal is to find the lengths of BM and DL.

Recalling the Formula for the Area of a Parallelogram

The area of a parallelogram can be calculated using the formula:

Area = base × height

In this case, the base of the parallelogram is AB, and the height is DL. However, we are also given the height BM, so we can use the formula:

Area = AD × BM

We can also use the formula:

Area = AB × DL

Setting Up the Equations

We can set up two equations using the formulas above:

1470 = 49 × BM ... (Equation 1) 1470 = 35 × DL ... (Equation 2)

Solving for BM

To solve for BM, we can divide both sides of Equation 1 by 49:

BM = 1470 ÷ 49 BM = 30

Solving for DL

To solve for DL, we can divide both sides of Equation 2 by 35:

DL = 1470 ÷ 35 DL = 42

Conclusion

In this problem, we were given a parallelogram ABCD with heights DL and BM on AB and AD respectively. We were also given the area of the parallelogram, which is 1470 sq cm, and the lengths of AB and AD, which are 35 cm and 49 cm respectively. Using the formulas for the area of a parallelogram, we were able to set up two equations and solve for the lengths of BM and DL. The length of BM is 30 cm, and the length of DL is 42 cm.

Key Takeaways

The area of a parallelogram can be calculated using the formula: Area = base × height
The base of the parallelogram can be either AB or AD
The height of the parallelogram can be either DL or BM
We can set up two equations using the formulas above and solve for the lengths of BM and DL

Real-World Applications

This problem has real-world applications in various fields such as architecture, engineering, and design. For example, in architecture, the area of a building can be calculated using the formula for the area of a parallelogram. In engineering, the area of a bridge or a beam can be calculated using the same formula. In design, the area of a product or a packaging can be calculated using the same formula.

Practice Problems

A parallelogram has an area of 1200 sq cm and a base of 40 cm. Find the height of the parallelogram.
A parallelogram has an area of 1800 sq cm and a height of 30 cm. Find the base of the parallelogram.
A parallelogram has a base of 50 cm and a height of 25 cm. Find the area of the parallelogram.

Solutions

To find the height of the parallelogram, we can use the formula: Area = base × height. We can divide both sides of the equation by the base to get: height = Area ÷ base. Plugging in the values, we get: height = 1200 ÷ 40 = 30.
To find the base of the parallelogram, we can use the formula: Area = base × height. We can divide both sides of the equation by the height to get: base = Area ÷ height. Plugging in the values, we get: base = 1800 ÷ 30 = 60.
To find the area of the parallelogram, we can use the formula: Area = base × height. Plugging in the values, we get: Area = 50 × 25 = 1250.

Conclusion

Q: What is a parallelogram?

A: A parallelogram is a type of quadrilateral with opposite sides that are parallel to each other. It has two sets of parallel sides, and the opposite angles are equal.

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

A: The formula for the area of a parallelogram is: Area = base × height. This formula can be used to calculate the area of a parallelogram when the base and height are known.

Q: How do I find the height of a parallelogram?

A: To find the height of a parallelogram, you can use the formula: height = Area ÷ base. This formula can be used to calculate the height of a parallelogram when the area and base are known.

Q: How do I find the base of a parallelogram?

A: To find the base of a parallelogram, you can use the formula: base = Area ÷ height. This formula can be used to calculate the base of a parallelogram when the area and height are known.

Q: What is the difference between a parallelogram and a rectangle?

A: A parallelogram is a type of quadrilateral with opposite sides that are parallel to each other, while a rectangle is a type of parallelogram with four right angles. All rectangles are parallelograms, but not all parallelograms are rectangles.

Q: Can a parallelogram have a right angle?

A: Yes, a parallelogram can have a right angle. In fact, a rectangle is a type of parallelogram with four right angles.

Q: Can a parallelogram have a obtuse angle?

A: Yes, a parallelogram can have an obtuse angle. In fact, a parallelogram can have any angle measure, as long as the opposite angles are equal.

Q: How do I find the length of the diagonal of a parallelogram?

A: To find the length of the diagonal of a parallelogram, you can use the Pythagorean theorem. The diagonal of a parallelogram divides it into two right triangles, and the length of the diagonal can be found using the formula: diagonal = √(base² + height²).

Q: Can a parallelogram have a diagonal that is equal to the base?

A: No, a parallelogram cannot have a diagonal that is equal to the base. The diagonal of a parallelogram is always greater than the base.

Q: Can a parallelogram have a diagonal that is equal to the height?

A: No, a parallelogram cannot have a diagonal that is equal to the height. The diagonal of a parallelogram is always greater than the height.

Q: What is the relationship between the area of a parallelogram and its diagonal?

A: The area of a parallelogram is equal to the product of the base and the height, while the diagonal of a parallelogram is equal to the square root of the sum of the squares of the base and the height.

Q: Can a parallelogram have a diagonal that is equal to the sum of the base and the height?

A: No, a parallelogram cannot have a diagonal that is equal to the sum of the base and the height. The diagonal of a parallelogram is always greater than the sum of the base and the height.

Conclusion

In this article, we answered some frequently asked questions about parallelograms. We discussed the formula for the area of a parallelogram, how to find the height and base of a parallelogram, and the relationship between the area and diagonal of a parallelogram. We also answered some additional questions about parallelograms, including how to find the length of the diagonal and whether a parallelogram can have a diagonal that is equal to the base or height.