In parallelogram ABCD, height BM splits side AD into segments AM and DM find the area if BD = 15cm BC = 16 AM = 7cm

univerkov | July 6, 2021 | education

1. According to the properties of a parallelogram, its opposite sides are equal.

Therefore, BC = AD = 16 centimeters.

2. DM = AD – AM = 16 – 7 = 9 centimeters.

3. We calculate the length of the BM height using the formula of the Pythagorean theorem:

BM = √BD ^ 2 – DM ^ 2 = √15 ^ 2 – 9 ^ 2 = √225 – 81 = √144 = 12 centimeters.

4. The area of the parallelogram = AD x BM = 16 x 12 = 192 centimeters ^ 2.

Answer: the area of the parallelogram ABCD is 192 centimeters ^ 2.

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