In parallelogram abcd, ad = 12 in, m∠c = 46º, m∠dba = 72º. find the area of abcd

The area of   parallelogram ABCD  is

Explanation:

Given:

AD = 12 in

To Find:

The area of   parallelogram ABCD=?  

Solution:

When we construct the parallelogram with the given data, we get a parallelogram formed by 12 cm as one side and an angle with 46 degrees.  

The area of the parallelogram can be calculated by

Substituting the value of a=12  we have

To find  the value of b,

We know that area of a triangle can be expressed as,

So,

Cancelling BD and 2 on both sides we get,  

Therefore,

Substituting the value of b,

=78.42  

So the area of the parallelogram is

an = 22 + (n-1) *6

110 seats

step-by-step explanation:

an=a1+(n-1)(d)

a1 = 22   this is the first item in the sequence

d =6   this is how the sequence goes up

a)   an = 22 + (n-1) *6

b) a12 = 22 + (12-1) *6

    a12 = 22+11*6

  a12 = 22 +88

  a12 = 110