ABCD Is A Parallelogram In Which AB=8cm, AD= 6.4cm And DM= 6cm (a) Find The Area Of Parallelogram (b) Find The Length Of BN.​

(a) Find the area of parallelogram

To find the area of the parallelogram ABCD, we need to use the formula for the area of a parallelogram, which is given by:

Area = base × height

In this case, we are given the length of the base (AB) as 8cm and the length of the perpendicular from D to AB (DM) as 6cm. However, we need to find the height of the parallelogram, which is the length of the perpendicular from A to the line containing the base.

Since DM is the perpendicular from D to AB, we can use the Pythagorean theorem to find the length of the perpendicular from A to AB.

Let's denote the length of the perpendicular from A to AB as AM. Then, we can use the Pythagorean theorem as follows:

AM² + DM² = AD²

Substituting the given values, we get:

AM² + 6² = 6.4²

AM² + 36 = 40.96

AM² = 4.96

AM = √4.96 ≈ 2.23cm

Now that we have the height of the parallelogram, we can find the area using the formula:

Area = base × height

Area = 8 × 2.23

Area ≈ 17.84cm²

(b) Find the length of BN

To find the length of BN, we need to use the properties of a parallelogram. Since ABCD is a parallelogram, we know that the opposite sides are equal and parallel.

Let's denote the length of BN as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

8 = x + 6.4

Subtracting 6.4 from both sides, we get:

1.6 = x

Therefore, the length of BN is 1.6cm.

Conclusion

In this problem, we were given a parallelogram ABCD with certain measurements and asked to find the area and the length of BN. We used the properties of a parallelogram and the Pythagorean theorem to find the height of the parallelogram and then used the formula for the area of a parallelogram to find the area. We also used the properties of a parallelogram to find the length of BN.

Key Takeaways

• The area of a parallelogram can be found using the formula: Area = base × height
• The height of a parallelogram can be found using the Pythagorean theorem
• The opposite sides of a parallelogram are equal and parallel
• The length of a segment in a parallelogram can be found using the properties of a parallelogram

Practice Problems

• Find the area of a parallelogram with a base of 10cm and a height of 5cm
• Find the length of a segment in a parallelogram with a base of 8cm and a height of 3cm
• Find the area of a parallelogram with a base of 12cm and a height of 4cm

Solutions to Practice Problems

• Find the area of a parallelogram with a base of 10cm and a height of 5cm:

Area = base × height = 10 × 5 = 50cm²

• Find the length of a segment in a parallelogram with a base of 8cm and a height of 3cm:

Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

8 = x + 3

Subtracting 3 from both sides, we get:

5 = x

Therefore, the length of the segment is 5cm.

• Find the area of a parallelogram with a base of 12cm and a height of 4cm:

Area = base × height = 12 × 4 = 48cm²

Q&A

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

A: The formula for the area of a parallelogram is given by: Area = base × height

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

A: To find the height of a parallelogram, we can use the Pythagorean theorem. Let's denote the length of the perpendicular from A to AB as AM. Then, we can use the Pythagorean theorem as follows:

AM² + DM² = AD²

Q: What is the relationship between the opposite sides of a parallelogram?

A: The opposite sides of a parallelogram are equal and parallel.

Q: How do we find the length of a segment in a parallelogram?

A: To find the length of a segment in a parallelogram, we can use the properties of a parallelogram. Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

Q: What is the area of a parallelogram with a base of 10cm and a height of 5cm?

A: The area of a parallelogram with a base of 10cm and a height of 5cm is given by:

Area = base × height = 10 × 5 = 50cm²

Q: What is the length of a segment in a parallelogram with a base of 8cm and a height of 3cm?

A: The length of a segment in a parallelogram with a base of 8cm and a height of 3cm is given by:

Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

8 = x + 3

Subtracting 3 from both sides, we get:

5 = x

Therefore, the length of the segment is 5cm.

Q: What is the area of a parallelogram with a base of 12cm and a height of 4cm?

A: The area of a parallelogram with a base of 12cm and a height of 4cm is given by:

Area = base × height = 12 × 4 = 48cm²

Q: How do we find the length of BN in a parallelogram?

A: To find the length of BN in a parallelogram, we can use the properties of a parallelogram. Let's denote the length of BN as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

8 = x + 6.4

Subtracting 6.4 from both sides, we get:

1.6 = x

Therefore, the length of BN is 1.6cm.

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

A: The area of a parallelogram is directly proportional to its base and height. The formula for the area of a parallelogram is given by: Area = base × height

Q: How do we use the Pythagorean theorem to find the height of a parallelogram?

A: To find the height of a parallelogram, we can use the Pythagorean theorem. Let's denote the length of the perpendicular from A to AB as AM. Then, we can use the Pythagorean theorem as follows:

AM² + DM² = AD²

Q: What is the significance of the height of a parallelogram?

A: The height of a parallelogram is an important concept in geometry. It is used to find the area of a parallelogram and to determine the length of segments in a parallelogram.

Q: How do we use the properties of a parallelogram to find the length of a segment?

A: To find the length of a segment in a parallelogram, we can use the properties of a parallelogram. Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

Q: What is the relationship between the opposite sides of a parallelogram and the length of a segment?

A: The opposite sides of a parallelogram are equal and parallel. This property is used to find the length of a segment in a parallelogram.

Q: How do we find the area of a parallelogram with a given base and height?

A: To find the area of a parallelogram with a given base and height, we can use the formula: Area = base × height

Q: What is the significance of the area of a parallelogram?

A: The area of a parallelogram is an important concept in geometry. It is used to determine the size of a parallelogram and to compare the sizes of different parallelograms.

Q: How do we use the properties of a parallelogram to find the length of a segment?

A: To find the length of a segment in a parallelogram, we can use the properties of a parallelogram. Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

Q: What is the relationship between the opposite sides of a parallelogram and the length of a segment?

A: The opposite sides of a parallelogram are equal and parallel. This property is used to find the length of a segment in a parallelogram.

Q: How do we find the area of a parallelogram with a given base and height?

A: To find the area of a parallelogram with a given base and height, we can use the formula: Area = base × height

Q: What is the significance of the area of a parallelogram?

A: The area of a parallelogram is an important concept in geometry. It is used to determine the size of a parallelogram and to compare the sizes of different parallelograms.

Q: How do we use the properties of a parallelogram to find the length of a segment?

A: To find the length of a segment in a parallelogram, we can use the properties of a parallelogram. Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

Q: What is the relationship between the opposite sides of a parallelogram and the length of a segment?

A: The opposite sides of a parallelogram are equal and parallel. This property is used to find the length of a segment in a parallelogram.

Q: How do we find the area of a parallelogram with a given base and height?

A: To find the area of a parallelogram with a given base and height, we can use the formula: Area = base × height

Q: What is the significance of the area of a parallelogram?

A: The area of a parallelogram is an important concept in geometry. It is used to determine the size of a parallelogram and to compare the sizes of different parallelograms.

Q: How do we use the properties of a parallelogram to find the length of a segment?

A: To find the length of a segment in a parallelogram, we can use the properties of a parallelogram. Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

Q: What is the relationship between the opposite sides of a parallelogram and the length of a segment?

A: The opposite sides of a parallelogram are equal and parallel. This property is used to find the length of a segment in a parallelogram.

Q: How do we find the area of a parallelogram with a given base and height?

A: To find the area of a parallelogram with a given base and height, we can use the formula: Area = base × height

Q: What is the significance of the area of a parallelogram?

A: The area of a parallelogram is an important concept in geometry. It is used to determine the size of a parallelogram and to compare the sizes of different parallelograms.

Q: How do we use the properties of a parallelogram to find the length of a segment?

A: To find the length of a segment in a parallelogram, we can use the properties of a parallelogram. Let's denote the length of the segment as x. Then, we can use the fact that the opposite sides of a parallelogram are equal to write:

AB = CD

Q: What is the relationship between the opposite sides of a parallelogram and the length of a segment?

A: The opposite sides of a parallelogram are equal and parallel. This property is used to find the length of a segment in a parallelogram.

Q: How do we find the area of a parallelogram with a given base and height?

A: To find the area of a parallelogram with a given base and height, we can use the formula: Area = base × height

Q: What is the significance of the area of a parallelogram?

A: The area of a parallelogram is an