11.2 Areas of Triangles, Trapezoids, and Rhombi
Objectives• Find areas of triangles
• Find areas of trapezoids
• Find areas of rhombi
Area of Triangles• If the triangle has the area of A
square units, a base of b units, and a height of h units, then…
A=1/2bhA
B
Cb
h
Example 1:Find the area of the triangle if the base
is 9 in. and the height is 5 in.
A=1/2bh
B
A
C
9
5
Example 1:Since the base is 9 in. and the height is 5 in.
your equation should read,
A=1/2(5x9) Solve
A=1/2(45) Multiply.
A=22.5 Multiply by ½.
The area of triangle ABC is 22.5 square inches.
Area of Quadrilaterals Using Δ's
The area of a quadrilateral is equal to the sum of the areas of triangle FGI and triangle GHI.
A (FGHI)= ½(bh) + ½(bh)
F
g
G
I H
Example 2:Find the area of the quadrilateral if FH= 37 in.
18 in.
9 in.
FG
I H
Example 2:A= ½(37x9)+ ½(37x18) Solve.
A= ½(333) + ½(666) Multiply.
A= 166.5 + 333 Add.
A= 499.5 square inches
Area of a TrapezoidIf a trapezoid has an area of A units,
bases of b1 units and b2 units and a height of h units, then…
A= ½ h (b1+b2)h
b2
b1
Example 3:Find the area of the trapezoid.
12 yd.
16 yd.
24 yd.
14 yd.
Example 3:A= ½x12(16+24) Add.
A= ½x12(40) Multiply.
A= ½(480) Multiply.
A= 240 square yards.
Example 4:Area of a trapezoid
on the coordinate plane.
Since TV and ZW are horizontal, find their length by subtracting the x-coordinates from their endpoints.
T V
Z W
(-3,4) (3,4)
(-5,-1) (6,-1)
Example 4:TV= |-3-3|TV= |-6|TV= 6
ZW= |-5-6|ZW= |-11|ZW= 11Because the bases are horizontal segments, the distance between them can be measured on a vertical line. That is, subtract the y-coordinates.
H= |4-(-1)| H= |5|H= 5
Example 4:Now that you have the height and bases, you can
solve for the area.
A= ½h(b1+ b2)
A= ½(5)(6+11) Substitution.
A= ½(5)(17) Addition.
A= ½(85) Multiply.
A= 42.5 square units.
Area of RhombiIf a rhombus has an area of A square
units and diagonals of d1 and d2 units, then…
A= ½(d1xd2) (AC is d1, BD is d2)
A
B
DC
d1d2
Example 5:Find the area of the rhombus if ML=
20m and NP= 24m.
M
L
N
P
Example 5:A= ½(20x24) Multiply.
A= ½(480) Multiply.
A= 240 Square meters.
Rhombus on Coordinate Plane
To find the area of a rhombus on the coordinate plane, you must know the diagonals.
To find the diagonals...subtract the x-coordinates to find d1, and subtract
the y-coordinates to find d2.
Example 6:Find the area of a rhombus with the
points E(-1,3), F(2,7), G(5,3), and H(2,-1) F (2,7)
G (5,3)
H (2,-1)
E (-1,3)
Let EG be d1 and FH be d2Subtract the x-
coordinates of E and G to find d1
d1= |-1-5|d1= |-6|d1= 6
Subtract the y-coordinates of F and H to find d2
d2= |7-(-1)|d2= |8|d2= 8
F (2,7)
G (5,3)
H (2, -1)
E (-1,3)
d1
d2
Now that you have D1 and D2, solve.
A= ½(d1xd2)
A= ½(6x8) Multiply.
A= ½(48) Multiply.
A= 24 sq. units.
Find the Missing Measures Rhombus WXYZ has an area of 100
square meters. Find XZ if WY= 20 meters. X
Y
Z
W
Use the formula for the area of a rhombus and solve for D1 (XZ)
A= ½(d1xd2)
100= ½(d1)(20) Substitution.
100= 10(d1) Multiply.
10=d1 Divide.
XZ= 10 meters
Postulate 11.1Postulate 11.1: Congruent figures have
equal areas.
Assignment:• Pre-AP
Pg. 606 #13-21, 22-28 evens, 30-35
• GeometryPg. 606 #13 – 21, 30 - 35
