abcd is a parallelogram with sides ab=12 cm,bc=10 cm and diagonal ac=16 cm .find the area of the parallelogram also find the distance between its shortest sides
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To find the area of the parallelogram ABCD, we can use the formula:
Area = base * height
In this case, since the given sides AB and BC are adjacent sides of the parallelogram, we can take AB as the base and the distance between AB and CD as the height.
To find the distance between AB and CD, we can use the Pythagorean theorem since AB and AC are the two sides of a right triangle with AC as the hypotenuse.
1. Find the length of AD using the Pythagorean theorem:
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
AD^2 + AB^2 = AC^2
AD^2 + 12^2 = 16^2
AD^2 + 144 = 256
AD^2 = 256 - 144
AD^2 = 112
AD = √112 = 10.58 cm (rounded to two decimal places)
2. The distance between AB and CD is equal to the length of AD.
Distance = AD = 10.58 cm
3. Find the area of the parallelogram using the formula:
Area = base * height
Area = AB * Distance
Area = 12 cm * 10.58 cm
Area ≈ 126.96 cm² (rounded to two decimal places)
Therefore, the area of the parallelogram ABCD is approximately 126.96 cm² and the distance between its shortest sides (AB and CD) is approximately 10.58 cm.