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

Question

Andreas93 [3]

2 years ago

7

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.

Mathematics

1 answer:

jeyben [28] · Answer 1 · 2022-05-25T22:42:43+03:00

Answer:

Step-by-step Explanation:

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.