Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).

iohanetc 2021-06-11 Answered

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).

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Expert Answer

un4t5o4v
Answered 2021-06-12 Author has 105 answers
Jeffrey Jordon
Answered 2021-09-28 Author has 2581 answers

Consider the parallelogram A=(-3;0), B(-1,5), C(7;4) and D=(5;-1)

The objective is to find the area of parallelogram

Find the are as follows:

The area of the parallelogram is the magnitude of the cross product of the adjacent edges.

That is, Area=|AB×AD|

Find the adjacent edges AB and AD as follows

AB=BA

=(1;5)(3;0)

=(1+3;50)

=(2;5)

AD=DA

=(5;1)(3;0)

=(8;1)

Find AB×AD as,

AB×AD=[ijk250810]

=5(0)0(1)i(2(0)0(8))j+(2(1)5(8))k

=0i+0j42k

The area of the parallelogram is,

Area =|AB×AD|

=|(0i+0j42k|

=(0)2+(0)2+(42)2

=(42)2

= 42 square unit

Hence, the area of parallelogram is 42

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