ABCD is a parallelogram and AM is the perpendicular from A to BC and AN is the perpendicular from A to CD.If AB is 6,3cm ,AD 4,9cm and AN 4,2cm.Calculate the area of the parallelogram.Hence Find AM
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Consider CD as a base. CD=AB = 6.3
Now, AN is the altitude from CD.
So the area of ABCD is 6.3*4.2 = 26.46
Now you know that BC*AM = 26.46
You know BC=AD=4.9, so now find AM.
To find the area of the parallelogram, we can use the formula A = base * height.
The base of the parallelogram is AB, which is given as 6.3 cm.
The height of the parallelogram is AN, which is given as 4.2 cm.
Therefore, the area of the parallelogram is A = 6.3 cm * 4.2 cm = 26.46 cm^2.
To find AM, we can use the Pythagorean theorem.
In triangle AMN, we have:
AN^2 = AM^2 + MN^2
Substituting the given values, we have:
4.2^2 = AM^2 + MN^2
Solving for AM, we have:
AM^2 = 4.2^2 - MN^2
AM^2 = 4.2^2 - (AD)^2
AM^2 = 4.2^2 - 4.9^2
AM^2 = 17.64 - 24.01
AM^2 = -6.37
Since AM cannot be negative, it seems there may be an error in the given information.
To calculate the area of a parallelogram, we need to know the base and height of the parallelogram.
In this case, we have the base AB, which is given as 6.3 cm. However, we do not have the height.
To find the height, we can use the perpendiculars AM and AN. Since AM is the perpendicular from A to BC, it is also the height of the parallelogram.
We are given that AN is 4.2 cm. Since AM is perpendicular to BC, it forms a right triangle with BC and AN. The height AM is the hypotenuse of this right triangle.
Using the Pythagorean theorem, we can calculate the height AM.
AM^2 = AB^2 - AN^2
AM^2 = (6.3 cm)^2 - (4.2 cm)^2
AM^2 = 39.69 cm^2 - 17.64 cm^2
AM^2 = 22.05 cm^2
Taking the square root of both sides, we get:
AM ≈ 4.7 cm
Now that we have the height, we can calculate the area of the parallelogram.
Area of parallelogram = base × height
Area = AB × AM
Area = 6.3 cm × 4.7 cm
Area ≈ 29.61 cm^2
Therefore, the area of the parallelogram is approximately 29.61 cm^2 and the height AM is approximately 4.7 cm.