Page 133 - Math Course 1 (Book 2)

Area: Triangles, Rhombi, And Trapezoids

Postulate 10.1 A = d d Area of a rhombus
1
2
1 2
Congruent f gures have equal areas.
1
= (3 )(5 ) or 15 d = 3 , d = 5 22 2
2
2 1 2
Check The area of rhombus MNPR is 15 square
Let’s Begin units.

Answer 15 square units
Area of a Rhombus on a Coordinate Plane

Example

Find Missing Measures
Find the area of rhombus MNPR with vertices at
M(0, 1), N(4, 2), P(3, –2), and R(–1, –3).
Example
y
N(4, 2) Rhombus RSTU has an area of 64 square inches.
Find US if RT = 8 inches.
M(0, –1)
Use the formula for the area of a rhombus and
0 x solve for d .
2

1
R(–1,–3) P(3,–2) A = d d R S
2
1 2
1
64 = (8)(d )
Explore To f nd the area of the rhombus, we need 2 2
to know the lengths of each diagonal.
64 = 4d
2
U T
Plan Use coordinate geometry to f nd the 16 = d
length of each diagonal. Use the formula 2
to f nd the area of rhombus MNPR

Solve Let MP be d and NR be d . Answer 16 inches
1
2
Use the Distance Formula to f nd MP.

d = (x –x ) + (y –y ) 2 Real World Example
2
1 2 1 2 1
= (0 – 3) + [1–(–2)] 2
2
STAINED GLASS
= 18 or 3 2 This stained glass window is composed of 8
congruent trapezoidal shapes. The total area of
Use the Distance Formula to f nd NR. the design is 72 square feet. Each trapezoid has
bases of 3 and 6 feet. Find the height of each
2
d = (x –x ) + (y –y ) 2
1 2 1 2 1 trapezoid.
= [4 – (–1)] + [2–(–3)] 2
2
= 50 or 5 2

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