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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.

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Presentation on theme: "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."— Presentation transcript:

1 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 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 Youll Need 10-2

2 FeatureLesson Geometry Lesson Main 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 units 2. 1212 1212 1212 Solutions Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Check Skills Youll Need 10-2

3 FeatureLesson Geometry Lesson Main 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 units 2. 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 units 2. 1212 1212 1212 1212 1212 1212 1212 1212 Solutions (continued) Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Check Skills Youll Need 10-2

4 FeatureLesson Geometry Lesson Main 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 ft 2 24 square units 6 cm 15 m 2 Lesson 10-1 Areas of Parallelograms and Triangles Lesson Quiz 10-2

5 FeatureLesson Geometry Lesson Main Textbook

6 FeatureLesson Geometry Lesson Main

7 FeatureLesson Geometry Lesson Main Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Notes 10-2 The height of a trapezoid is the perpendicular distance h between the bases.

8 FeatureLesson Geometry Lesson Main Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Notes 10-2

9 FeatureLesson Geometry Lesson Main A car window is shaped like the trapezoid shown. Find the area of the window. A = 504Simplify. The area of the car window is 504 in. 2 A = h(b 1 + b 2 )Area of a trapezoid 1212 A = (18)(20 + 36)Substitute 18 for h, 20 for b 1, and 36 for b 2. 1212 Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Quick Check Additional Examples 10-2 Real-World Connection

10 FeatureLesson Geometry Lesson Main Find the area of trapezoid ABCD. Draw an altitude from vertex B to DC that divides trapezoid ABCD into 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 Kites Additional Examples 10-2 Finding the Area Using a Right Triangle

11 FeatureLesson Geometry Lesson Main (continued) By the Pythagorean Theorem, BX 2 + XC 2 = BC 2, so BX 2 = 13 2 – 5 2 = 144. Taking the square root, BX = 12 ft. You may remember that 5, 12, 13 is a Pythagorean triple. A = 162Simplify. The area of trapezoid ABCD is 162 ft 2. A = h(b 1 + b 2 )Use the trapezoid area formula. 1212 A = (12)(11 + 16)Substitute 12 for h, 11 for b 1, and 16 for b 2. 1212 Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Quick Check Additional Examples 10-2

12 FeatureLesson Geometry Lesson Main Find the lengths of the diagonals of kite XYZW. XZ = d 1 = 3 + 3 = 6 and YW = d 2 = 1 + 4 = 5 A = 15Simplify. The area of kite XYZW is 15 cm 2. A = d 1 d 2 Use the formula for the area of a kite. 1212 A = (6)(5)Substitute 6 for d 1 and 5 for d 2. 1212 Find the area of kite XYZW. Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Quick Check Additional Examples 10-2 Finding the Area of a Kite

13 FeatureLesson Geometry Lesson Main Find the area of rhombus RSTU. Lesson 10-2 Areas 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

14 FeatureLesson Geometry Lesson Main 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 = 120Simplify. The area of rhombus RSTU is 120 ft 2. A = d 1 d 2 Area of a rhombus 1212 A = (24)(10)Substitute 24 for d 1 and 10 for d 2. 1212 Lesson 10-2 Areas 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

15 FeatureLesson Geometry Lesson Main 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 cm 2 26 square units 94.5 3 in. 2 100 2 m 2 840 mm 2 Lesson 10-2 Areas of Trapezoids, Rhombuses, and Kites Lesson Quiz 10-2


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