We can consider the side whose length is 33.5 centimeters as the base. However, we need to find the height. To do so, we will pay close attention to the right triangle formed by the height, a side, and a part of a nonparallel side.
We can see that the measure of two of the interior angles of the triangle are 45^(∘) and 90^(∘). We can use the Triangle Angle Sum Theorem to find the measure of the third angle.
180^(∘)- 90^(∘)- 45^(∘)=45^(∘)
The third angle measures 45^(∘) and, therefore, we have a 45^(∘)-45^(∘)-90^(∘) triangle. In this type of triangle, the legs are congruent. With this information, and knowing that the length of the one leg is 10.1cm, we know that the second leg measures 10.1cm. This is also the measure of the height of our parallelogram.
Now that we know that the base is 33.5cm and that the height is 10.1cm, we can substitute these values in the formula for the area of a parallelogram.
