
Find the area of a parallelogram given in Figure. Also find the length of the altitude from vertex A on the side DC. (in )

Answer
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Hint: To find the area of a parallelogram . First determine the area of a triangle using Heron's formula . Also determine the area of parallelogram by using the formula to find the length of the altitude from vertex A on the side DC.
Complete step-by-step answer:
We know that the diagonal of a parallelogram divides it into two congruent triangles.
So, area of a parallelogram .
Here, we will find the area of
According to Heron’s formula the area of a triangle with sides a, b, & c is given as –
.
Where,
.
Here, we have from the figure –
So, we will get the value of s as –
Now, we will put the value of a, b, c and s in the formula to find .
Since ABCD is a parallelogram,
Now, we will find the area of parallelogram.
Area of a parallelogram .
Area of a parallelogram
Next we will find the altitude of a parallelogram be h.
Let us consider the altitude of a parallelogram to be ‘h’.
Also, area of a parallelogram
We know that the altitude of a parallelogram is also known as Height of a parallelogram.
Therefore,
Height of altitude from vertex A on side CD of the parallelogram .
Hence, the area of a parallelogram for the given figure is and the altitude from vertex A on side CD is 15 cm.
Note: We have taken the area of both triangles as the same here, but if a student doesn't know that, they can find it separately and then add them together. The mistake of finding an area of parallelogram as should be avoided, it is not correct at all. A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Opposite sides of a parallelogram are parallel and so will never intersect.
Complete step-by-step answer:
We know that the diagonal of a parallelogram divides it into two congruent triangles.
So, area of a parallelogram
Here, we will find the area of
According to Heron’s formula the area of a triangle with sides a, b, & c is given as –
Where,
Here, we have from the figure –

So, we will get the value of s as –
Now, we will put the value of a, b, c and s in the formula
Since ABCD is a parallelogram,
Now, we will find the area of parallelogram.
Area of a parallelogram
Next we will find the altitude of a parallelogram be h.
Let us consider the altitude of a parallelogram to be ‘h’.
Also, area of a parallelogram
We know that the altitude of a parallelogram is also known as Height of a parallelogram.
Therefore,
Height of altitude from vertex A on side CD of the parallelogram
Hence, the area of a parallelogram for the given figure is
Note: We have taken the area of both triangles as the same here, but if a student doesn't know that, they can find it separately and then add them together. The mistake of finding an area of parallelogram as
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