Area of Quadrilaterals

Slides:

Advertisements

Similar presentations

Triangles, Trapezoids & Kites

Advertisements

Area Formulas Rectangle What is the area formula?

Areas of Rectangles and Parallelograms Areas of Triangles, Trapezoids and Kites.

11 – 6f Area, Surface Area & Volume

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Developing Formulas for Triangles and Quadrilaterals

Section 8.5. Find the area of parallelograms. Base of a parallelogram Height of a parallelogram Parallelogram Rhombus.

Using Area Formulas You can use the postulates below to prove several theorems. AREA POSTULATES Postulate 22 Area of a Square Postulate Postulate 23 Area.

Quadrilaterals Bryce Hall 4 Wennersten.

Parallelograms, Trapezoids and Triangles Section

9-1 Developing Formulas for Triangles and Quadrilaterals Warm Up

Area of Quadrilaterals SECTION After completing this lesson, you will be able to say: I can use composition and decomposition to determine the area.

Relationships in Geometry Friday January 31st. Objective for today. I understand where we are headed in this unit. I can tell you what we will be covering.

6-7 Area of Triangles and Quadrilaterals Warm Up Lesson Presentation

Unit 10 Review Area Formulas. FOR EACH FIGURE: IMAGINE the shape THINK of its AREA FORMULA.

Polygons with 4 sides and 4 angles

Quadrilaterals By Billy Hudson 4/14/05 Geometry 4 th period.

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

Area of Triangles and Trapezoids

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=

Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. (2, 5), (6, 17) (-2, 3), (4, 6) (7, -3), (4, 10)

6.7 Area of Triangles and Quadrilaterals

Area Formulas Rectangle What is the area formula?

Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c √3.

Holt CA Course Perimeter & Area of Parallelograms MG2.1 Use formulas routinely for finding the perimeter and area of basic two- dimensional figures.

9-2 Area of Triangles and Trapezoids Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson.

Area of Quadrilateral.

Area of a Parallelogram

10-2 Areas of Trapezoids, Rhombuses & Kites Objective: To find the area of a trapezoid, rhombus or kite Essential Understanding You can find the area of.

What you will learn? Formulas for finding the areas of rectangles, parallelograms, triangles, trapezoids, kites, regular polygons, and circles by cutting.

Given the parallelogram at right, we are able to determine that its area is equal to Activity You can use a parallelogram to find the area of a triangle.

Quadrilaterals MA1G3d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square,

A parallelogram with opposite equal acute and obtuse angles and four equal sides. Diagonals 4 equal sides.

Lesson 6.3/6.4 Objective: To find the two missing lengths of a 30°- 60°- 90°triangle. To classify four sided polygons. In a 30°-60°-90° triangle, The hypotenuse.

Learn about the quadrilaterals Understand the different types of quadrilaterals Students and Teachers will be able to.

Quadrilaterals Objective: Learn to name and classify quadrilaterals.

A quadrilateral is any 2- dimensional, four- sided shape.

Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles and special.

Area. Triangles and rectangles are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. Each line segment forms.

9-3: Classifying Polygons Logic Activity. I am a trapezoid I have two angles that each measure 45˚ I have two other angles that each measure 135˚ #1)

Finding the Area of Polygons Rectangles Parallelograms Triangles Trapezoids.

QUADRILATERALS SPI: Identify, define or describe geometric shapes given a visual representation or written description of its properties.

Warm up Lisa says it is possible to draw a triangle that has more than one right angle. Miguel says that is impossible. Who is correct? Explain your answer.

6.7 Area of Triangles and Quadrilaterals Area Postulates: Postulate 22 Area of a Square: The area of a square is the square of the length of its side,

Four sided polygon Foldable 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line.

Geometry – Triangles and Trapezoids.  All Triangles are related to rectangles or parallelograms : Each rectangle or parallelogram is made up of two triangles!

How Can You Tell That All Four of These Figures Are Quadrilaterals? What do they all have in common?

Holt McDougal Geometry 10-1 Developing Formulas Triangles and Quadrilaterals 10-1 Developing Formulas Triangles and Quadrilaterals Holt Geometry Warm Up.

 0-10 pts.) Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of.

Area of Triangles and Trapezoids

Objectives Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles.

10-1 Developing Formulas Triangles and Quadrilaterals Warm Up

Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

10-1 Developing Formulas Triangles and Quadrilaterals Warm Up

9-1 Developing Formulas for Triangles and Quadrilaterals Warm Up

Area of Quadrilaterals

Objectives Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles.

6.7 Areas of Triangles and Quadrilaterals

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Finding the Area of Triangles

A tangram is an ancient Chinese puzzle made from a square

Areas of Quadrilaterals and Triangles

9-1 Developing Formulas for Triangles and Quadrilaterals Warm Up

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Area of a a parallelogram

Properties of Quadrilaterals

Presentation transcript:

Area of Quadrilaterals

Objectives I can find the areas of parallelograms, rhombuses, and trapezoids.

Area of a Parallelogram What is a parallelogram? -a quadrilateral in which opposite sides are parallel and congruent.

How do we find the area of a parallelogram? In front of you is a parallelogram on the paper. Cut it out Cut your parallelogram along the dotted line. Now move your triangular piece to the other side of the parallelogram.

What figure have you formed? Rectangle Does it have the same area as the parallelogram? Base of the parallelogram is equal to The length of a rectangle The height of the parallelogram is equal to The width of a rectangle

Area of parallelogram continued Area of parallelogram is equal to Area of rectangle How do we find the area of a rectangle? Area = product of the length and width Area = length times width A=(l)(w) How do we find the area of a parallelogram? Area = the product of the base and height Area = base time height A = bh

Find the area ! The base of my parallelogram is 13 inches and the height is 9 inches. Find the area. A = bh A = 13 · 9 117 inches squares Why are the units squared? We are multiplying and inch by an inch. This is no different than multiplying 2 time 2 which can be written as 2²

Math Talk On a piece of paper answer the following: How is the relationship between the length and width of a rectangle similar to the relationship between the base and height of a parallelogram?

Trapezoid What is a trapezoid? A quadrilateral in which two sides are parallel.

Finding the area of a trapezoid Look at the two congruent trapezoids. What do you notice? You should notice that the two trapezoids can fit together to form a parallelogram. How does the trapezoid compare to the parallelogram? It is half of it.

If the trapezoid is half the parallelogram, then the area of the trapezoid is? The height of the parallelogram is the same as the height of the trapezoid. The base of the parallelogram is the sum of the two bases of the trapezoid. The Area of the trapezoid is found by adding base 1 and base 2 and multiplying it by ½ the height Area of a Trapezoid = 1/2h(b₁ +b₂)

Try some! A section of deck is in the shape of a trapezoid, what is the area of this section of deck if base one is 15 feet, base 2 is 25 feet and the height is 21 feet. Area of a Trapezoid = 1/2h(b₁ +b₂) Area = ½ · 21 (15 + 25) 420 ft²

Math Talk On your piece of paper. Answer the following. Does it matter which of the trapezoids bases is substituted for b₁ and which is substituted for b₂? Why or Why not?

Rhombus A rhombus is a quadrilateral in which all sides are congruent and opposite sides are parallel. Can a square be classified as a rhombus? Yes, all side are congruent and opposite side are parallel. Some people call a rhombus a Diamond or a kite A diagonal is a line that can be drawn from one vertices to the opposite vertices.

Area of a rhombus A rhombus can be divided into four triangles. Go ahead and cut your rhombus into 4 triangles. Rearrange them into another shape. Rectangle The base of the rectangle is the same length as one of the diagonals of the rhombus. The height of the rectangle is ½ the length of the other diagonal.

Rhombus Formula The area of a rhombus is half of the product of its two diagonals. A = 1/2·d₁ · d₂

Try one! Cedric is constructing a kite in the shape of a rhombus. The spars (wood pieces that fabric attaches to. These would be the diagonals) of the kite measure 15 inches and 24 inches. How much fabric will Cedric need for the kite? A = 1/2d₁d₂ A= ½ · 15 · 24 A= 180 in²

Looking at the formulas What were all the formulas based upon? The parallelogram or rectangle.

Higher Order Thinking Answer the following: Simon says that to find the area of a trapezoid, you can multiply the height by the top base and by the bottom base, then add the two products together and divide the sum by 2. Is Simon correct? Explain your answer.

Advanced Multistep The height of a trapezoid is 8 in. and its area is 96 in². One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases. Explain how you found your answer.

Multistep The height of a trapezoid is 8 in. and its area is 96 in². One base of the trapezoid is 6 inches long. What is the length of the other base. Explain how you found your answer.

Practice