.--
G.GMD.7 WORKSHEET #4
-
6.*.r\
NAME:
PATTERSON
1. What is the definition of a trapezoid?
OSU AS LT or
A Q"*pglu\141AL tNtl4 gXAcZuY oNeSYz
?trt+t-r-Ee 9toa;s. 'XALTLT
2. A trapezoid can bri dhought of
is
(-lrro>'I
oFPoSlTL
a composite shape (a shape made up of smaller more basic shapes).
Dissect the trapezoid into the required shapes.
b) Rectangle &
a)Two Triangles
Triangle
c) Parallelogram and
d)Two Triangles and
Triangle
Rectangle
a
It' mcrrrTHAN I +n s,^-e,
3. One way to demonstrate that the area formula for a trapezoid is A=lz (b1 + b2)h is using a DOUBLING
TECHNIQUE. Demonstrate how rotating a trapezoid on the midpoint of one of its non-base sides helps us
discover its formula for area. (Use patty paper to help you)
Sm^= 2 (rr.AtrzaroS\
= ( b,+ u) (x\
Arn*ee =
!t..(u,*br\
to cut the height of the trapezoid in half
(midpoints have been provided). How can this help us derive the formula for the area of a trapezoid? (Use
patty paper to help you.)
4. Another technique is the HAtVtNG TECHNIQUE. Use dissection
b1
\
h
t'ru
/
b2
bl
Ap^^=Ur\)(b,* b)
Ar* L= ,t*tu,+bz\
G.GMD.I WORKSHEET #4 -
PATTERSON
2
5. Use dissection to establish the area formula for a trapezoid. Create the relationship based on the
dissection and then transform that into the area formula for a trapezoid.
b) A Parallelogram and a Triangle
a) A Rectangle and a Triangle
,11br
b1
L\.
u' bz-bl
brl,. +
Ix(ur-u,\
ttul . |u,u -Qill
Ix(ur-u,\
r b,tr
SIHL
tT
h(br*brd)A Rectangle and Two Triangles
h.
br
br
4-x9
la1-bg-x
bz --------------)
(-
bz
[= ftr,^ + I.Urr^
)n(t
Aos.t
=
r
s
|rtr
t/
+ brh. + L*tbr-
b,
rt)
-/,
= )o,^ + +!'h
!x (u,+ u,
5. If a trapezoid is an isosceles trapezoid, it has two congruent legs and two sets of congruent base angles.
Use dissection
to determine the area formula.
Lose
bz-X =b,*x
be-br; Zx
b, -b.
?-
-':X
A = (r,*b--b'\r"
zt
=brh *n(r+,)
toehf
= b,h +
LZ
It,x + LUt
t..(bt+bz
G.GMD.7 WORKSHEET #4
-
PATTERSON
3
7. Determine the area of the foltowing trapezoids.
a)
b)
c)
,{
s
8cm
T (s ri)
(+\
Z
J-
z
= i8.S".^."
Area
Iz (.{) (1+s\
11 cm
(r\ rb)
(s\
12.S"^2
d)
Area
f)
no z
LO
cq
=
5cm
t2
cm 3'+x"= S'
x
L tq)(a +la\
Z
36
Area =
s)
^;
-2
x +E=[o
x e(.
2
"r
f ,tt (: + rr\
.U
Area= b I cm
2
1
Lzl4
a
h)
locm
Area
+ ro)1r
3
Fr)
= Z[ [-t .^t
1ry
i)
s
-
14 cm
14 cm
I
Z
* rq) (s)
50
Area
i)
(ro
x2 +32=
"
nnz
xg6
Area=
9t
k)
r{
ta?
t
15 cm
13
,
1
a12cm
x-+
".=;lr e tB-
Itrt(s+rr)
=
"^L
t38'
{tr"t(?+rr)
.*
zrli c*
12 cm
\
z
Area =
(*n) (rz + zo)
a
tl-3
.n" rrt
3f3 +
10 cm
I
Area
t.tl (ro +z)
= Z\ "rr3
zft + sR
I" t.t (sR +an)=
Area
= l5l? ",\
*tr)(orr)