7.4: Areas of Trapezoids, Rhombuses and Kites

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7.4: Areas of Trapezoids,
Rhombuses and Kites
Objectives:
•To find the area of a trapezoid, rhombus and kite.
•To use right triangles in finding area of geometric
figures
TRAPEZOID
b1
LEG
LEG
b2
 The height (h) is the perpendicular distance between
the bases
 b1 and b2 are the bases (the parallel sides)
AREA OF A TRAPEZOID
A
1
2

h b1  b 2
Find the area of the trapezoid:
12cm
7cm
15 cm

Find the area:
14 in
8 in
20 in.
Using Special Right Triangles to Find
Area:
5m
60°
7m
1. Draw in height
2. Use special right triangle relationship to find height
Find the area:
12 ft
45°
16 ft
If the area of a trapezoid is 112 m2, and the lengths
of the bases are 11 m and 21 m, what is the height?
Area of a RHOMBUS or a KITE
• Only one formula to know! It’s the same for
both!
Area = ½ the product of the lengths of the diagonals
Area =
1
2
d1  d 2
or
d1  d 2
2
PLEASE, PLEASE, PLEASE BE CAREFUL!!! IT IS THE
PRODUCT OF THE DIAGONALS, NOT THE SUM!!
RHOMBUS
d1
d2
KITE
d2
d1
Find the area of the kite:
1.
2.
3
2
3
5
4.5
10
2
4.5
Find the area of the Rhombus:
 What do we know about the
diagonals of a rhombus?
B
15 m
E
A
12 m
D
C
 Use the Pythagorean Theorem to
find the length of BE:

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