Answer :
Explanation:
To find the area of the parallelogram, you can use the formula:
Area = base * height
Since AC is the diagonal, it divides the parallelogram into two congruent triangles. You can use the Pythagorean theorem to find the height of one of these triangles:
\[ AC^2 = AB^2 + BC^2 \]
\[ 42^2 = 3^2 + 20^2 \]
\[ 1764 = 9 + 400 \]
\[ 1764 - 9 = 400 \]
\[ h^2 = 1764 - 9 \]
\[ h^2 = 1755 \]
\[ h = \sqrt{1755} \]
\[ h \approx 41.91 \, \text{cm} \]
Now, you have the height of the parallelogram. Multiply this by the base (AB) to get the area:
\[ \text{Area} = 3 \, \text{cm} \times 41.91 \, \text{cm} \]
\[ \text{Area} \approx 125.73 \, \text{cm}^2 \]
So, the area of the parallelogram is approximately \( 125.73 \, \text{cm}^2 \).