Transcript 11.2 Areas of Triangles, Trapezoids, and Rhombi

11.2 Areas of Triangles,
Trapezoids, and Rhombi
Area of a Triangle
If a triangle has an
area of A square
units, a base of b
units, and a
corresponding height
of h units, then
A= ½bh.
h
b
Area of a Triangle
A= ½bh
A= ½(8)(5)
5 cm
A= 20 cm2
8 cm
Areas of Triangles
Find the area of quadrilateral XYZW if XZ= 39, HW= 20, and YG= 21.
The area of the quadrilateral is equal to the sum of the areas of
triangle XWZ and triangle XYZ.
Y
H
X
G
W
Z
Areas of Triangles
Area of XYZW= area of
triangle XYZ+ area of triangle
XWZ
A= ½bh 1 + ½bh 2
A= ½(39)(21) = ½(39)(20)
A= 409.5 + 390
A= 799.5
XZ= 39, HW=20, YG=21
Y
H
X
G
The area of quadrilateral
XYZW is 799.5 square units.
W
Z
Area of a Trapezoid
If a trapezoid has an
area of A square
units, bases of b 1 ,
units and b 2 units, and
a height of h units,
then A= ½h(b 1+b 2).
b
1
h
b
2
Area of a Trapezoid
A= ½h(b 1+b 2)
A= ½(8)(14+9)
A= ½(8)(23)
A= 4(23)
2
A= 92 yd
14 yd
8 yd
9 yd
Area of a Rhombus
If a rhombus has an
area of A square unit
and diagonals of d 1
and d 2 units, then
A= ½d 1 d 2 .
A= ½(AC)(BD)
A
B
D
C
Area of a Rhombus
A= ½d 1d 2
A= ½(30)(24)
A= 380 in
2
15 in
12 in
12 in
15 in
Finding Missing Measures
Trapezoid PQRS has an area of 250 square
inches. Find the height of PQRS.
P
20 in
S
Q
R
30 in
Finding Missing Measures
Use the Formula for the area of
a trapezoid and solve for h.
20 in
A= ½h(b 1 +b 2)
250= ½h(20+30)
250= ½(50)h
250= 25h
10= h
P
S
R
30 in
The height of the trapezoid
PQRS is 10 inches.
Q
Assignment
Page 606
#13-21,#22-34 Evens