Question 1 Report
In the diagram above ABDE and FCDE are parallelograms. If |FC| = 12.2cm and the height |PC| = 4.0cm, calculate the area of the parallelogram ABDE.
We know that ABDE and FCDE are parallelograms which means their opposite sides are equal and parallel. Therefore, |AB| = |DE| and |AE| = |BD|. We can calculate the area of parallelogram ABDE as follows: Area of ABDE = |AB| x |PC| We need to calculate |AB| and we can do this by finding the length of |DE|. In parallelogram FCDE, the opposite sides |DE| and |FC| are equal. Therefore, |DE| = |FC| = 12.2cm. Also, we know that FCDE is a parallelogram, so the height |PC| is equal to the height of parallelogram ABDE. Now, we can find the length of |AB| using the Pythagorean theorem. |AB|2 = |AE|2 + |DE|2 |AB|2 = (4.0cm)2 + (12.2cm)2 |AB|2 = 149.24cm2 |AB| = 12.2cm Therefore, the area of ABDE is: Area of ABDE = |AB| x |PC| = 12.2cm x 4.0cm = 48.8cm2 Therefore, the answer is 48.8cm2.