Back to Lesson 7-5
Name
Name
7-4B
page 2
USES
Objective H: Find areas of triangles or
7-5A Lesson Master
SKILLS
trapezoids in real situations.
9. The Heslers live on a corner with three roads adjacent to their
house. Two of the roads cause the lawn on one side of the house
to be triangular. The Heslers want to re-sod that part of the lawn.
The width of the lawn along that side of the house is 100 feet. The
length of the triangular lawn, perpendicular to the edge of the
house to the point where the roads meet, is 60 feet. How much
sod does the family need to buy?
Questions on SPUR Objectives
See pages 480–483 for objectives.
Objective B
In 1 and 2, draw an altitude of the trapezoid.
60 ft
1.
2.
100 ft
Hesler house
3,000 ft2
In 3 and 4, find the area of the trapezoid.
10. An amateur ship builder is making sails for a large sailboat. One of the
two triangular sails will be 22 feet tall and 16 feet across the bottom.
The other sail will be 18 feet tall and 14 feet across the bottom. What
is the combined area of the two sails?
3.
302 ft2
14
4.
7
11. Steve wants to make a triangular pyramid with 4 faces. He takes
4 isosceles triangles and tapes them together. Each triangle is
4 inches wide at the bottom. The altitude of each triangle is
9 inches. What is the total area of the 4 triangular faces?
6
119 square units
120 square units
72 in2
5. Name three special types of trapezoids, draw a picture of each, and give its area formula.
b. What is the total uncolored area of the six faces of the cube?
h
h
s
w
60 square units
324 square units
a. What is the total area of the six triangles?
s
ℓ
Drawing
12. Brenda makes a cube using graph paper. Each face of the cube is an
8 × 8 grid. On each face, she colors a triangle that is 5 squares
wide and 4 squares tall.
b
Name
b
Formula
Answers may vary. Use any three:
Rectangle, A = ℓw; Parallelogram, A = bh; Square, A = s2; or Rhombus, A = bh
13. Carlos has 4 pieces of wood with a combined surface area of
80 square feet. He needs to rebuild one side of a skateboard
ramp with the dimensions shown. He can join pieces of wood
with metal braces, but the surface must be without any gaps.
6. Use the parallel lines at the right to draw 4 parallelograms
with different perimeters but the same area.
Sample:
6 ft
12 ft
8 ft
h
Yes
Yes; 20 square feet
a. Does Carlos have enough wood to rebuild the side of the ramp?
b. Will he have any wood left over? If so, what is the area
of the wood he will have left?
14. Bobby takes a piece of 8 __12 -in. by 11-in. paper
and folds the bottom over to the right side.
Then he bends down the top two corners to
create a shape with five sides. Find the area
of the new figure by subtracting the areas of
the three folded corners from the area of
the original rectangle. Show your work.
1 2
51 __
8 in
368
USES
'JSTUGPME
4FDPOEGPMET
50 ft
15 ft
15 ft
30 ft
20 ft
50 ft
710 km
8. Tennessee is roughly shaped like a trapezoid. Using the given
measures in the diagram at the right, estimate the area of
the state.
109,800 km2
Transition Mathematics
180 km
510 km
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Name
7-5B Lesson Master
6-5B
7-5B
SKILLS Objective B: Find the area of a trapezoid (including special
9. a. Use the parallel lines at the right to draw 2 parallelograms
with different perimeters, but the same area.
b. Explain why the two parallelograms you drew have the
same area.
types) given appropriate dimensions.
In 1 and 2, draw an altitude of the trapezoid.
page 2
The 2 parallelograms have equal
area because they have the same
base and the same height.
2.
In 3–8, a. Find the area of the trapezoid. b. Name the trapezoid if it is one
of the special types. Write “no” if it is not one of the special types.
USES
Objective H: Find areas of triangles or trapezoids
in real situations.
4.
5
4
8
5
25 square units
square
5.
a.
b.
26 square units
no
6.
GU
b.
105 square units
parallelogram
11. In a circus, platform boxes are used to showcase animal tricks.
One of the platforms has 4 sides each shaped like a trapezoid. The
platform is square on both the top and bottom. The top square is
16 inches on each side and the bottom square is 18 inches on each
side. The height along each side face of the platform is 12 inches.
a. What is the area of each side?
b. What was the total surface area of the six faces of the platform?
a.
b.
JO
204 in2
1,396 in2
#
14
a.
b.
98 square units
rectangle
a.
b.
15 square units
rhombus
12. Each side of a regular hexagon is 5 units long. The hexagon can be
cut into two trapezoids. It is given that AD = 11 and BF = 8,
bisected at G.
a. Find the area of trapezoid ABCD.
b. Find the area of the entire figure.
32 square units
a.
64
square units
b.
370
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a.
8.
7
3,900 ft2
1,674 ft2
JO
60 square units
no
b.
GU
7.
b.
45"(&
JO
a.
a.
GU
5
GU
10. a. The seating area in a theater is in the shape of a trapezoid.
The stage is 50 feet across at the front; the back row of seats is
70 feet wide. The seating area is 65 feet deep. What is the area of
the seating area?
b. The stage is also in the shape of a trapezoid. It is 50 feet wide at
the front and 43 feet wide at the back. The stage is 36 feet deep.
Find the area of the stage.
GU
3.
"
%
(
'
Transition Mathematics
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371
$
Copyright © Wright Group/McGraw-Hill
1.
b.
369
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Name
a.
30 ft
20 ft
64 ft
2,730 ft2
Objective H
7. The roof of the Bennett house is made up of two trapezoids
and two triangles, as shown at the right (top view). If they are
replacing the shingles, what is the area they will need to cover?
b
&
371
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