Geometry 11.3 Areas of Trapezoids.

Slides:

Advertisements

Similar presentations

Our lesson Area Trapezoids Confidential.

Advertisements

Quadrilaterals Project

Trapezoids A type of Quadrilateral. Review of Quadrilaterals ParallelogramHas two parallel pairs of opposite sides. RectangleHas two pairs of opposite.

Honors Geometry Section 4.5 (3) Trapezoids and Kites.

CP Geometry Mr. Gallo. What is a Trapezoid Trapezoid Isosceles Trapezoid leg Base Base Angles leg Base Angles If a quadrilateral is a trapezoid, _________________.

6.6 Trapezoids and Kites A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called bases. The.

6-6 Trapezoids and Kites.

Trapezoids and Kites Section 8.5.

Area of Quadrilaterals and Triangles. What is a quadrilateral? Any polygon with four sides and four vertices (or corners) All sides must be straight.

Perimeter The perimeter of a polygon is the sum of the lengths of the sides Example 1: Find the perimeter of  ABC O A(-1,-2) B(5,-2) C(5,6) AB = 5 – (-1)

4.6 – AREA FORMULAS. Formulas from yesterday: Perim.of a Rect.= Area of a Rect.=

8-4 Area of Triangles and Trapezoids Learn to find the area of triangles and trapezoids.

The Area of a Trapezoid Lesson 11.3 b2b2 b1b1 h. Theorem 102: The area of a trapezoid equals one-half the product of the height and the sum of the bases.

Areas of Trapezoids Geometry Unit 4, Lesson 2.

Trapezoids A quadrilateral with exactly one pair of parallel sides is called a trapezoid.

GEOMETRY – Area of Parallelogram, Rhombus, and Trapezoid A parallelogram is a 4 – sided figure created by two pairs of parallel sides. Opposite sides are.

Section 16.1 Pythagorean Theorem a=11.6. x=3.86 y=4.60 x=

GEOMETRY REVIEW Look how far we have come already!

Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.

Review & Trapezoids. Properties of a Parallelogram A BC D 1. Opposite sides are parallel. 2 Opposite sides are congruent. 3. Opposite angles are congruent.

Geometry 11.1 Areas of Rectangles.

Geometry Chapter 11 Review. Parallelogram A = bh Base Height.

How to Find the Area of a Parallelogram Step 1, Plan: To find the area of a parallelogram, use the formula A = bh.

5.11 Use Properties of Trapezoids and Kites. Vocabulary  Trapezoid – a quadrilateral with exactly one pair of parallel sides. Base Base Angle Leg.

Geometry Section 8.5 Use Properties of Trapezoids and Kites.

Geometry Section 6.5 Trapezoids and Kites. A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel. The sides that are parallel.

6-6 Trapezoids and Kites Objective: To verify and use properties of trapezoids and kites.

Warm-Up Find the area: 1.Square with side length 13 2.Triangle with hypotenuse 13 and leg 5 3.Rectangle with base 24 and height 15 4.Parallelogram with.

Warm Up’s. Area of Trapezoids Trapezoids b1b1 b2b2 h Trapezoids have 2 bases. They are the parallel sides. The height is determined by forming a.

Geometry 5.5 Trapezoids. Trapezoid (Defn.) Memo about medians A quadrilateral with exactly one pair of parallel sides. leg base The sides are called the.

Area of Trapezoids Tutorial 13c.

10-1: Area of Parallelograms and Triangles Objectives: To find the area of parallelograms and triangles To find the area of parallelograms and triangles.

Please click the speaker symbol on the left to hear the audio that accompanies some of the slides in this presentation. Quadrilaterals.

Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Quadrilaterals ParallelogramsRectangleRhombusTrapezoids Isosceles Trapezoid Squares Orange Book Page 14: Do you know the tree?

WARM UP Find the area of an equilateral triangle with sides 8 ft.

May 27,  A trapezoid is a quadrilateral with two parallel sides (called bases) and two nonparallel sides (called legs)

Trapezoids Euclidean Geometry High School Math Online.

Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 4.4 The Trapezoid.

Confidential1. 2 Find the area: 1. Base = 10 cm, height = 2 cm 2. Base = 6 m, height = 4 m Find the base of the triangle: 3. area = 96 cm 2, height =

Find the Area, Round to the nearest hundredth

Geometry 12.1 Prisms. Today you will learn how to find three measurements about prisms. You will find: Prisms Lateral area: L.A. Total area: T.A. Volume:

5.4 Quadrilaterals Objectives: Review the properties of quadrilaterals.

Use Properties of Trapezoids and Kites Lesson 8.5.

1 cm Area is the number of unit squares needed to cover a region or surface. Area.

Areas of Trapezoids, Rhombuses, and Kites Objective: 1.To find the areas of trapezoids, rhombuses, and kites.

How can you apply formulas for perimeter, circumference, and area to find and compare measures?

Lesson 11-3 Areas of Trapezoids (page 435) Essential Question How can you calculate the area of any figure?

6.5 Trapezoids and kites Base angles Isosceles trapezoids Midsegments.

8.5 Trapezoids. Parts of a Trapezoid Parts The bases of a trapezoid are the parallel sides The legs of the trapezoid connect the bases The base angles.

Chapter 11 Areas of Plane Figures (page 422)

Do Now: List all you know about the following parallelograms.

Section 11-5: Areas of Triangles & Trapezoids

Trapezoids Section 5-5.

Trapezoids Section 5-5.

Area and Perimeter: Trapezoids Keystone Geometry

Geometry Quick Discussion 10.1 Squares and Rectangles

SQUARE All sides equal Opposite sides parallel All angles are right

Lesson 6-5: Trapezoid & Kites

4.4 The Trapezoid A quadrilateral with exactly two parallel sides. The parallel sides are called the bases and the nonparallel sides are the legs. Median.

Chapter 7 Proofs and Conditional Probability

Lesson 6-5: Trapezoid & Kites

Areas of Parallelograms and Triangles

6.4 Rhombuses, Rectangles, and Squares 6.5 Trapezoids and Kites

Exercise 1 2 Evaluate xy when x = 7 and y =

Lesson 6-5 Trapezoids and Kites.

Fill in the following table – checking each characteristic that applies to the figures listed across the top; Characteristic Polygon Quadrilateral Parallelogram.

Areas of Parallelograms and Triangles

4.4 The Trapezoid A quadrilateral with exactly two parallel sides. The parallel sides are called the bases and the nonparallel sides are the legs. Median.

Presentation transcript:

Geometry 11.3 Areas of Trapezoids

Trapezoids In a trapezoid, the bases are the parallel sides. An altitude of a trapezoid is defined in the same way as an altitude of a parallelogram. The altitude of a trapezoid is any segment perpendicular to a line containing one base from a point on the opposite base. In a trapezoid, all altitudes have the same length, called the height, h. b1 h h h b2

A = ½h(b1+ b2) A = mh Area of a Trapezoid The area of a trapezoid equals half the product of height and the sum of the bases. b1 8 A = ½h(b1+ b2) 6 h or 12 A = mh b2 m is the median, the average of the bases Area = ½(6)(8 + 12) = 60 square units Area = 10(6) = 60 square units

Exercises 1. A = ½(11)(18+8) 3. A = ½(6√3)(30+15) A = 143 A = 135√3 Try # 2 and #4! 10 3 7 30º 8 2 8 11 18 15 12 30 60 45 10 6√3 8 6 2 1. A = ½(11)(18+8) 3. A = ½(6√3)(30+15) A = 143 A = 135√3 2. A = ½(10)(7+3) 4. A = ½(8)(10+2) A = 50 A = 48

Easy method : Find m first A = ½h(b1+ b2) m is the median length of the trapezoid m = ½ (b1+ b2) So, more simply: It is the average of the bases A = h•m

Exercises 5 3 15 6x 8 70 35 14 17.5 11.5 5.5 10x = h•m edian 6. 7. 8. 9. 10. b1 15 25 8 14x b2 13 10 9 h 5 4 7x A 140 46 70x2 m 7 5 3 15 6x 8 = h•m 70 35 edian 14 17.5 11.5 5.5 10x 7. 46 = 4m m = 11.5 11.5 = ½(8 + b2) 23 = 8 + b2 b2 = 15 9. 6√3m = 33√3 m = 5.5 5.5 = ½(b1 + 8) 11 = b1 + 8 b1 = 3 5. m = ½(15 + 13) m = 14 A = 5(14) = 70 6. m = ½(25 + 10) m = 17.5 140 = 17.5 h h = 8 8. 7 = ½(b1 + 9) 14 = b1 + 9 b1 = 5 10. 70x² = 7x • m m = 10x b1 = 6x

Exercises Find the area of each isosceles trapezoid. 5-12-13 Triple x 6 12 24 60 10 30 26 6√3 x 10 10 m = ½(24 + 12) x² + 10² = 26² m = ½(30+ 10) m = 18 x² + 100 = 676 m = 20 x² = 576 A = 6√3 • 18 A = 24 • 20 x = √576 A = 108√3 A = 480 x = 24

Exercises 13. Find the area of an isosceles trapezoid with legs 25 cm and bases 16 cm and 30 cm. 16 7-24-25 Triple 25 25 24 30 - 16 7 30 7 2 m = ½(16 + 30) 552 cm² m = 23 A = 24 • 23 = 552

Exercises 14. Find the area of a trapezoid with 45˚ base angles and bases 17 and 23. 17 45-45-90 Rt. ∆ 3√2 3 45 45 23 - 17 3 23 3 2 m = ½(17 + 23) m = 20 A = 3 • 20 = 60 60 sq. units

Homework pg. 436 #1-19, 23 odd pg. 470 #1-9 For #5 see the bonus from Powerpoint 11.2