# A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #pi/8 #, what is the area of the parallelogram?

Area of parallelogram

By signing up, you agree to our Terms of Service and Privacy Policy

To find the area of the parallelogram, we can use the formula:

[ \text{Area} = \text{base} \times \text{height} ]

In this case, we can take sides A and B as the base, and side C as the height, or vice versa. Since we know the length of sides A and B is 2, and the length of side C is 3, we can use the length of side C as the base, and the height as the perpendicular distance from side C to sides A and B.

To find the height, we can use trigonometry. Given that the angle between sides A and C is ( \frac{\pi}{8} ), we can use the sine function:

[ \sin\left(\frac{\pi}{8}\right) = \frac{\text{opposite}}{\text{hypotenuse}} ]

The opposite side is the height we are looking for, and the hypotenuse is side A or B (since they are equal). Thus:

[ \text{Height} = \sin\left(\frac{\pi}{8}\right) \times 2 ]

Now, we have the base and the height, so we can calculate the area of the parallelogram:

[ \text{Area} = 3 \times \sin\left(\frac{\pi}{8}\right) \times 2 ]

Compute the value of ( \sin\left(\frac{\pi}{8}\right) ), then multiply it by 3 and 2 to find the area of the parallelogram.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- The vertices of the trapezoid are J(4m, 4n), K(4q, 4n), M(4p, 0), and L(0, 0). How do you find the midpoint of the midsegment of the trapezoid Midsegment=HN?
- You are given that the angles of a quadrilateral taken in order are #2x^6, 3x^6, 7x^6# and #6x^6#. Can you say which type of quadrilateral it is?
- Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #54 #, how long are the other two sides?
- What are the properties of parallelograms?
- Two opposite sides of a parallelogram each have a length of #2 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #3 #, how long are the other two sides?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7