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11-2 Objectives
You will learn to:
Find the area of trapezoids and rhombi.
Discover the Area of Trapezoid
We can divide the trapezoid into two triangles.
b1
The area of each triangle is:
A = ½(b • h)
So the area for the
trapezoid is:
A = ½(b1 • h) + ½(b2 • h)
b2
or
A = ½(h)(b1 + b2)
Area of a Trapezoid
Find Measurements
Find the area of a trapezoid in which b1 = 8 in.,
b2 = 5 in., and h = 6.2 in.
Area of a trapezoid
Substitute 8 for b1, 5 for b2,
and 6.2 for h.
A = 40.3 in2
Simplify.
Find the area of trapezoid RSTU with vertices R(4, 2),
S(6, –1), T(–2, –1), and U(–1, 2).
Bases: Since
and
are
horizontal, find their length
by subtracting the
x-coordinates of their
endpoints.
Height: Because the bases are
horizontal segments, the
distance between them can
be measured on a vertical
line. That is, subtract the ycoordinates.
Area:
Area of a trapezoid
Simplify.
Answer: The area of trapezoid RSTU is 19.5 square units.
Find the area of trapezoid WXYZ with vertices W(–3, 0),
X(1, 0), Y(2, –3), and Z(–5, –3).
b1 = 4
b2 = 7
h=3
A = ½(h)(b1 + b2)
A = ½(3)(4 + 7)
Answer:
Remember!
The diagonals of a rhombus or kite are
perpendicular, and the diagonals of a
rhombus bisect each other.
Kite Measurements
Find d2 of a kite in which d1 = 14 in. and
A = 238 in2.
Area of a kite
Substitute 238 for A and 14 for d1.
34 = d2
Solve for d2.
d2 = 34
Sym. Prop. of =
Find the area of rhombus MNPR with vertices at M(0, 1),
N(4, 2), P(3, –2), and R(–1, –3).
Explore To find the area of the
rhombus, we need to
know the lengths of
each diagonal.
Plan
Use coordinate
geometry to find the
length of each
diagonal. Use the
formula to find the
area of rhombus
MNPR.
Solve
Use the Distance Formula to find
.
Use the Distance Formula to find
.
Answer:
The area of rhombus MNPR is 15 square units.
Rhombus RSTU has an area of 64 square inches.
Find
if
inches.
Use the formula for the
area of a rhombus and
solve for d2.
Answer: US is 16 inches long.
Trapezoid DEFG has an area of 120 square feet.
Find the height of DEFG.
Use the formula for the area of a trapezoid and solve for h.
Answer: The height of trapezoid DEFG is 8 feet.
STAINED GLASS This stained glass window is
composed of 8 congruent trapezoidal shapes. The
total area of the design is 72 square feet. Each
trapezoid has bases of 3 and 6 feet. Find the height
of each trapezoid.
First, find the area of one trapezoid.
The area of each trapezoid is the
same. So, the area of each trapezoid
is
or 9 square feet.
Next, use the area formula to find the
height of each trapezoid.
STAINED GLASS This stained glass window is
composed of 8 congruent trapezoidal shapes. The
total area of the design is 72 square feet. Each
trapezoid has bases of 3 and 6 feet. The area of each
trapezoid is 9 square feet.
Area of a trapezoid
Substitution
Add.
Multiply.
Divide each side by 4.5.
Answer: Each trapezoid has a height of 2 feet.
What did you learn today?
How to:
Find the area of trapezoids and
rhombi.
Assignment:
Page 605
15 – 18, 23 – 29 odd, 30, 31