Question

Find the area of the parallelogram ABCD, where DC= 10 cm, AD = 6 cm, and A = 30 Degrees

Answer 1

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

\[
\text{Area} = b \cdot h
\]

where \( b \) is the base and \( h \) is the height. However, since we have an angle, we can also use the following formula:

\[
\text{Area} = b \cdot a \cdot \sin(A)
\]

where:
- \( b \) is the length of the base (in this case, \( DC \)),
- \( a \) is the length of the adjacent side (in this case, \( AD \)),
- \( A \) is the angle between the base and the adjacent side.

Given:
- \( DC = 10 \, \text{cm} \) (which is the base),
- \( AD = 6 \, \text{cm} \) (which is the length of the side adjacent to the base),
- \( A = 30^\circ \).

Now we can substitute these values into the area formula:

\[
\text{Area} = DC \cdot AD \cdot \sin(30^\circ)
\]

We know that \( \sin(30^\circ) = \frac{1}{2} \), so we can calculate:

\[
\text{Area} = 10 \, \text{cm} \cdot 6 \, \text{cm} \cdot \frac{1}{2}
\]

\[
\text{Area} = 10 \cdot 6 \cdot 0.5
\]

\[
\text{Area} = 60 \cdot 0.5 = 30 \, \text{cm}^2
\]

Thus, the area of the parallelogram ABCD is \( \boxed{30 \, \text{cm}^2} \).