Page 128 - Math Course 1 (Book 2)

Geometric Area: Parallelogram

Opposite sides have the same slope, so they are Perimeter of ABCD Def nition of
parallel. ABCD is a parallelogram. The slopes of = AB + BC + CD + AD perimeter
the consecutive sides are negative reciprocals of
each other, so the sides are perpendicular. Thus, = + + + 10 Substitution.
40
40
10
the parallelogram is a rectangle. In order for the
rectangle to be a square, all sides must be equal. Simplify
Use the Distance Formula to f nd the side lengths. = 2 + + 2 + 10
10
10
10
radicals.
2
2
AB = (x –x ) + (y –y ) 2 BC = (x –x ) + (y –y ) 2 Add like
2 1 2 1 2 1 2 1 = 6 10
terms.
2
= (1–3) + [4–(–2)] 2 = (–2–1) + [3–4] 2
2
Answer 6 10
= 40 = 10
Since AB ≠ BC, rectangle ABCD is not a square. C. The vertices of a quadrilateral are A(–2, 3),
B(4, 1), C(3, –2), and D(–3, 0).

Find the area of quadrilateral ABCD.
Answer rectangle

A(–2, 3)

B(4, 1)
B. Find the perimeter of quadrilateral ABCD.

For the previous question, we found that the f gure is
a rectangle by proving the opposite sides to be parallel D(–3, 0)
and the consecutive sides to be perpendicular. To
show that the f gure was not a square, we found that C(3, –2)
the lengths of consecutive sides were not congruent.

A(–2, 3)
Base: The base is AB, which we found to be
B(4, 1)
40

Height The height is BC, which we found to be
10
D(–3, 0)
C(3, –2) A = bh Area formula

10
40
40
= ( ) b = , h = 10
40
We found that AB = and BC = 10
= 400 Multiply
Since opposite sides are congruent, the lengths of = 20 Simplify.

CD and AD are also and , respectively.
10
40
Add to f nd the perimeter. Answer 20 square units

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