Feature Lesson Geometry Lesson Main (For help, go to Lesson 10-1.) 1. rectangle 2. a triangle 3. 4. 5. Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites the formula for the area of each type of figure. he area of each trapezoid by using the formulas for area ectangle and area of a triangle. Check Skills You’ll Need Check Skills You’ll Need 10-2
FeatureLesson Geometry Lesson Main (For help, go to Lesson 10-1.) 1. rectangle2. a triangle 3. 4. 5. Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites.
Mar 27, 2015
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FeatureLesson
GeometryGeometry
LessonMain
(For help, go to Lesson 10-1.)
1. rectangle 2. a triangle
3. 4.
5.
Lesson 10-2
Areas of Trapezoids, Rhombuses, and Kites Areas of Trapezoids, Rhombuses, and Kites
Write the formula for the area of each type of figure.
Find the area of each trapezoid by using the formulas for area of a rectangle and area of a triangle.
Check Skills You’ll Need
Check Skills You’ll Need
10-2
FeatureLesson
GeometryGeometry
LessonMain
1. A = bh
2. A = bh
3. Draw a segment from S perpendicular to UT. This forms a rectangle and a triangle.
The area A of the triangle is bh = (1)(2) = 1. The area A of the rectangle is
bh = (4)(2) = 8. By Theorem 1-10, the area of a region is the sum of
the area of the nonoverlapping parts. So, add the two areas: 1 + 8 = 9 units2.
12
12
12
Solutions
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Check Skills You’ll Need
10-2
FeatureLesson
GeometryGeometry
LessonMain
4. Draw two segments, one from M perpendicular to CB and the other from K
perpendicular to CB. This forms two triangles and a rectangle between them.
The area A of the triangle on the left is bh = (1)(2) = 1. The area A of
the triangle on the right is bh = (2)(2) = 2. The area A of the rectangle is
bh = (2)(2) = 4. By Theorem 1–10, the area of a region is the sum of the area
of the nonoverlapping parts. So, add the three areas: 1 + 2 + 4 = 7 units2.
5. Draw two segments, one from A perpendicular to CD and the other from B
perpendicular to CD. This forms two triangles and a rectangle between them.
The area A of the triangle on the left is bh = (2)(3) = 3. The area A of the
triangle on the right is bh = (3)(3) = 4.5. The area A of the rectangle is
bh = (2)(3) = 6. By Theorem 1–10, the area of a region is the sum of the area of the nonoverlapping parts. So, add the three areas: 3 + 4.5 + 6 = 13.5 units2.
12
121
212
12
12
12
12
Solutions (continued)
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Check Skills You’ll Need
10-2
FeatureLesson
GeometryGeometry
LessonMain
1. Find the area of the parallelogram.
2. Find the area of XYZW with vertices X(–5, –3), Y(–2, 3), Z(2, 3) and W(–1, –3).
3. A parallelogram has 6-cm and 8-cm sides. The height corresponding to the 8-cm base is 4.5 cm. Find the height corresponding to the 6-cm base.
4. Find the area of RST.
5. A rectangular flag is divided into four regions by its diagonals. Two of the regions are shaded. Find the total area of the shaded regions.
187 in.2
150 ft2
24 square units
6 cm
15 m2
Lesson 10-1
Areas of Parallelograms and TrianglesAreas of Parallelograms and Triangles
Lesson Quiz
10-2
FeatureLesson
GeometryGeometry
LessonMain Textbook
FeatureLesson
GeometryGeometry
LessonMain
FeatureLesson
GeometryGeometry
LessonMain
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Notes
10-2
The height of a trapezoid is the perpendicular distance h between the bases.
FeatureLesson
GeometryGeometry
LessonMain
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Notes
10-2
FeatureLesson
GeometryGeometry
LessonMain
A car window is shaped like the trapezoid shown.
Find the area of the window.
A = 504 Simplify.
The area of the car window is 504 in.2
A = h(b1 + b2) Area of a trapezoid12
A = (18)(20 + 36) Substitute 18 for h, 20 for b1, and 36 for b2.12
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Quick Check
Additional Examples
10-2
Real-World Connection
FeatureLesson
GeometryGeometry
LessonMain
Find the area of trapezoid ABCD.
Draw an altitude from vertex B to DC that divides trapezoid ABCDinto a rectangle and a right triangle.
Because opposite sides of rectangle ABXD are congruent, DX = 11 ft and XC = 16 ft – 11 ft = 5 ft.
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Additional Examples
10-2
Finding the Area Using a Right Triangle
FeatureLesson
GeometryGeometry
LessonMain
(continued)
By the Pythagorean Theorem, BX 2 + XC2 = BC2, so BX 2 = 132 – 52 = 144. Taking the square root, BX = 12 ft. You may remember that 5, 12, 13 is a Pythagorean triple.
A = 162 Simplify.
The area of trapezoid ABCD is 162 ft2.
A = h(b1 + b2) Use the trapezoid area formula.12
A = (12)(11 + 16) Substitute 12 for h, 11 for b1, and 16 for b2.12
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Quick Check
Additional Examples
10-2
FeatureLesson
GeometryGeometry
LessonMain
Find the lengths of the diagonals of kite XYZW.
XZ = d1 = 3 + 3 = 6 and YW = d2 = 1 + 4 = 5
A = 15 Simplify.
The area of kite XYZW is 15 cm2.
A = d1d2 Use the formula for the area of a kite.12
A = (6)(5) Substitute 6 for d1 and 5 for d2.12
Find the area of kite XYZW.
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Quick Check
Additional Examples
10-2
Finding the Area of a Kite
FeatureLesson
GeometryGeometry
LessonMain
Find the area of rhombus RSTU.
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
To find the area, you need to know the lengths of both diagonals.
Draw diagonal SU, and label the intersection of the diagonals point X.
Additional Examples
10-2
Finding the Area of a Rhombus
FeatureLesson
GeometryGeometry
LessonMain
The diagonals of a rhombus bisect each other, so TX = 12 ft.
You can use the Pythagorean triple 5, 12, 13 or the Pythagorean Theorem
to conclude that SX = 5 ft.
SU = 10 ft because the diagonals of a rhombus bisect each other.
A = 120 Simplify.
The area of rhombus RSTU is 120 ft2.
A = d1d2 Area of a rhombus12
A = (24)(10) Substitute 24 for d1 and 10 for d2.12
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
(continued)
SXT is a right triangle because the diagonals of
a rhombus are perpendicular.
Quick Check
Additional Examples
10-2
FeatureLesson
GeometryGeometry
LessonMain
1. Find the area of a trapezoid with bases 3 cm and 19 cm and height 9 cm.
2. Find the area of a trapezoid in a coordinate plane with vertices at (1, 1), (1, 6), (5, 9), and (5, 1).
Find the area of each figure in Exercises 3–5. Leave your answers in simplest radical form.
3. trapezoid ABCD
4. kite with diagonals 20 m and 10 2 m long
5. rhombus MNOP
99 cm2
26 square units
94.5 3 in.2
100 2 m2
840 mm2
Lesson 10-2
Areas of Trapezoids, Rhombuses, and KitesAreas of Trapezoids, Rhombuses, and Kites
Lesson Quiz
10-2
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