[30 pts] For the given parallelogram, AP is an angle bisector of ∠A, AP ⊥ BP ,AB = 15 cm, and BP = 9 cm. Find the perimeter and the area of the parallelogram.

Extend the sides AD and BP. This creates 2 congruent triangles using ASA. Triangles CBP and adjacent triangle are also congruent bc of ASA. This makes 3 congruent triangles (transitivity). That means just finding the area of the constructed large triangle, you find the area of the parallelogram. Since point P is the midpoint of B_, P_ also equals 9. Using the formula for the area of a triangle, and Pythagorean theorem (9-12-15), 12*18/2=108, which is the area of the parallelogram.   Hope this helps.

Extend the sides AD and BP. This creates 2 congruent triangles using ASA. Triangles CBP and adjacent triangle are also congruent bc of ASA. This makes 3 congruent triangles (transitivity). That means just finding the area of the constructed large triangle, you find the area of the parallelogram. Since point P is the midpoint of B_, P_ also equals 9. Using the formula for the area of a triangle, and Pythagorean theorem (9-12-15), 12*18/2=108, which is the area of the parallelogram