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# Step-by-Step Math Answer

Recall the formula for the area of a parallelogram.

The area of a parallelogram with base
*
b
*
and height
*
h
*
is given by

*
A
*
=
*
bh
*
.

Use the data for parallelogram
*
F
*
.

Parallelogram
*
F
*
has an area of 8
*
x
*
^{
2
}
+ 10
*
x
*
– 3 square meters and a height of 2
*
x
*
+ 3 meters. Substitute (8
*
x
*
^{
2
}
+ 10
*
x
*
– 3) for
*
A
*
and (2
*
x
*
+ 3) for
*
h
*
.

(8
*
x
*
^{
2
}
+ 10
*
x
*
– 3) =
*
b
_{
F
}
*
(2

*x*+ 3)

Solve for
*
b
_{
F
}
*
.

Divide each side by 2
*
x
*
+ 3.

Factor.

Factor.

Divide by the common factors.

Divide the numerator and the denominator by the common factors.

Simplify.

Simplify.

4
*
x
*
– 1 =
*
b
_{
F
}
*

Use the data for parallelogram
*
G
*
.

Parallelogram
*
G
*
has an area of 6
*
x
*
^{
2
}
+ 13
*
x
*
– 5 square meters and a height of 3
*
x
*
– 1 meters. Substitute (6
*
x
*
^{
2
}
+ 13
*
x
*
– 5) for
*
A
*
and (3
*
x
*
– 1) for
*
h
*
.

(6
*
x
*
^{
2
}
+ 13
*
x
*
– 5) =
*
b
_{
G
}
*
(3

*x*– 1)

Solve for
*
b
_{
G
}
*
.

Divide each side by 2
*
x
*
+ 3.

Factor.

Factor.

Divide by the common factors.

Divide the numerator and the denominator by the common factors.

Simplify.

Simplify.

2
*
x
*
+ 5 =
*
b
_{
G
}
*

Recall the formula for the area of a triangle.

The area of a triangle with base
*
b
*
and height
*
h
*
is given by

Substitute for right triangle H.

The base of right triangle H is
*
b
_{
G
}
*
and its height is

*b*. Substitute (2

_{ F }*x*+ 5) for

*b*and (4

*x*– 1) for

*h*.

Use the FOIL method.

Use the FOIL method.

Combine like terms.

Combine like terms.