Practice Problems on Diagonal of Parallelogram Formula

1. A parallelogram has sides of length 5 cm and 12 cm. One of the interior angles is 90° (making it a rectangle). Find the length of the diagonals.

2. A parallelogram has sides of length 8 cm and 10 cm. The angle between these sides is 60°. Find the length of one diagonal.

3. A parallelogram has sides of length 7 cm and 9 cm. One of the interior angles is 135°. Find the length of one diagonal.

4. One diagonal of a parallelogram is 15 cm. A side adjacent to this diagonal is 8 cm. If the angle between them is 45°, find the length of the other side of the parallelogram.

Diagonal of Parallelogram Formula: A parallelogram is a quadrilateral with equal pairs of opposite sides and angles. One of its pairs of opposite sides is parallel to the other. The interior angles lying are supplementary, that is, their sum is 180 degrees. The diagonals of a parallelogram bisect each other, that is, they divide each other into two equal parts. The sum of all interior angles of a parallelogram is 360 degrees.

The above figure depicts a parallelogram ABCD with sides AB, BC, CD, and AD and diagonals AC and BD. Here the lengths of opposite sides AB and CD are equal to each other. Similarly, the lengths of BC and AD are the same. The pairs of opposite angles, that is, ∠A and ∠C and ∠B and ∠D are equal to each other.