Area of Quadrilaterals

Slides:



Advertisements
Similar presentations
Yes you do need to write this.
Advertisements

Area Formulas Rectangle What is the area formula?
Area Formulas.
Area of Quadrilaterals
Bell Work: Quinn runs a sandwich shop
Mathematics 2D Shapes.
Types of Number – Squares, Cubes and their Roots
Volume of prisms and cylinders
Mathematics Compound Units - Speed.
Quadrilaterals Bryce Hall 4 Wennersten.
Area of Rectangles, Squares, Parallelograms, Triangles, and Trapezoids.
MATHEMATICS Area of Rectilinear Shapes. Lesson Objectives The aim of this powerpoint is to help you… practice using the formulas for the areas of rectangles.
Area of Quadrilaterals SECTION After completing this lesson, you will be able to say: I can use composition and decomposition to determine the area.
Area of Quadrilaterals and Triangles. What is a quadrilateral? Any polygon with four sides and four vertices (or corners) All sides must be straight.
Mathematics Simple Angle Facts.
Area of Rectangles and Triangles
Area and Perimeter.
Copyright©amberpasillas2010. Perimeter – (P) (P) The distance around a figure. 10 ft. 6 ft ft.
A tangram is an ancient Chinese puzzle made from a square
Area of shapes © T Madas.
Unit 10 Review Area Formulas. FOR EACH FIGURE: IMAGINE the shape THINK of its AREA FORMULA.
CHAPTER 23 Quadrilaterals. Special Quadrilaterals 1. Square a) All sides are the same length b) All angles are the same size (90°) c) Its diagonals bisect.
Volume of cubes and cuboids
© T Madas.
Areas of Parallelograms and Triangles
This presentation is based on KEY MATHS 7 (1) Press the LEFT mouse button to move on.
What is area? The amount of space that a figure encloses
Bell Work: Simplify √50. Answer: 5√2 LESSON 75: AREA OF A TRAPEZOID.
Perimeter Of Shapes. 8cm 2cm 5cm 3cm A1 A2 16m 12m 10m 12cm 7cm.
What is area? The amount of space that a figure encloses The number of square units that covers a shape or figure. It is two-dimensional It is always.
Area and Volume Using formulae. Finding Area and Perimeter of a Square or Rectangle Area is the measure of the amount of space a shape covers Perimeter.
Area of Squares, Rectangles, Parallelograms, and Triangles.
Area Formulas Rectangle What is the area formula?
A parallelogram has opposite sides and opposite angles equal.
Area.
Mr Barton’s Maths Notes
Warm Up Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = b = 21, c = a = 20, c = 52 c.
Area of a Parallelogram
Mathematics Surface Area.
What you will learn? Formulas for finding the areas of rectangles, parallelograms, triangles, trapezoids, kites, regular polygons, and circles by cutting.
MATHEMATICS Short Multiplication. The aim of this powerpoint is to teach you pencil & paper methods for multiplying large numbers by a single digit. EITHER.
Finding the area of parallelograms and trapeziums
Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles and special.
Finding the Area of Polygons Rectangles Parallelograms Triangles Trapezoids.
Area & Perimeter Learning Objectives: 1.Learn to find perimeter and area of simple & compound/composite shapes. 2.Practice solving problems involving area.
Geometry – Triangles and Trapezoids.  All Triangles are related to rectangles or parallelograms : Each rectangle or parallelogram is made up of two triangles!
Unit A Measurement & Shapes. Lesson 1: Rulers, Lengths, and Partner Lengths.
Area Formulas Rectangle What is the area formula?
Sect. 6.7 Areas of Triangles and Quadrilaterals Goal 1 Using Area Formulas Goal 2 Areas of Trapezoids, Kites and Rhombuses.
What is a Quadrilateral? A polygon with 4 sides!.
Announcements Finish factoring expressions Study for quiz over: Writing addition and subtraction expressions Writing and expanding multiplication expressions.
Objectives Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles.
Perimeter, area and volume
What is a Quadrilateral?
Area Formulas.
Area of Rectangles, Squares, Parallelograms, Triangles, and Trapezoids
Parallelograms and Trapezoids
Area of Polygons.
Mr F’s Maths Notes Shape and Space 5. Area.
Area of Quadrilaterals
Mr Barton’s Maths Notes
Area Review.
Finding the Area of Triangles
Areas of Quadrilaterals and Triangles
Mr Barton’s Maths Notes
Mr Barton’s math Notes 5. Area
Perimeter, area and volume. A A A A A A Contents S8 Perimeter, area and volume S8.1 Perimeter S8.6 Area of a circle S8.2 Area S8.5 Circumference of a.
Area Review.
Presentation transcript:

Area of Quadrilaterals Mathematics Area of Quadrilaterals

Lesson Objectives The aim of this powerpoint is to help you… calculate the area of parallelograms calculate the area of kites calculate the area of trapezia

Area Area is the amount inside a 2D (flat) shape. REMINDER: Area is the amount inside a 2D (flat) shape. Area is calculated by multiplying 2 perpendicular dimensions (distances) together The unit types must be the same before multiplying and therefore result in square units

Quadrilaterals Quadrilaterals are 4-sided shapes They include… rectangles; squares (special types of rectangles); parallelograms; rhombuses (special types of parallelograms); trapezia; kites; deltas (which you don’t need to learn). You should know: Area of a rectangle = length × width

Parallelograms A parallelogram is like a tilted rectangle BUT you do NOT multiply the longer side by the shorter side as these are NOT perpendicular to each other! However, if we cut one corner off and put it at the other end, we can make a rectangle. The area of the parallelogram which is now a rectangle has not changed, but now we can calculate the area!

Area Formula for Parallelogram The length of the rectangle formed is the base of the original parallelogram The width of the rectangle formed is the perpendicular height of the parallelogram (NOT the slanting side!) The area of this new rectangle, and therefore the area of the parallelogram is: base × perpendicular height slant perp. height base perp. height slant base

Quick Practice Calculate the area of this parallelogram… 6cm 4.5cm 8cm Area = base × perp. height So Area = 8cm × 4.5cm = 36cm²

What next? Print out the notes called PAV2b-AreaQ. Read through them and make sure you answer any questions on the areas of parallelograms. Work through the MyMaths lesson and its online homework called Area of a Parallelogram found at: http://app.mymaths.co.uk/267-resource/area-of-a-parallelogram http://app.mymaths.co.uk/267-homework/area-of-a-parallelogram Save and complete the worksheet called AreaP-S1.xlsx Now continue to work through this powerpoint

Kites The diagonals in a kite run vertically and horizontally so they are perpendicular Look at the diagram again We can re-arrange a kite into a rectangle shape The length and width of the rectangle are the longer diagonal and ½ of the shorter diagonal of the original kite.

Area Formula for a Kite Therefore the area of a kite is its diagonals multiplied together then divided by 2 i.e. A = ½ of d1 × d2 long diagonal ½ of the short diagonal

Quick Practice Calculate the area of this kite… 8.5m 10m 13m 19m Area = ½ of diagonal 1 × diagonal 2 So Area = ½ of (19 × 10) = ½ of 190 = 95m²

Squares & Rhombuses You can use the formula for the area of a rectangle for finding the area of a square. You can use the formula for the area of a parallelogram for finding the area of a rhombus. However, the diagonals of a square and of a rhombus cross at 90° so you can use the formula for calculating the area of a kite for them too! Area = length × width Area = base × p.height Area = ½ of diagonal 1 × diagonal 2

Formula Triangles Remember that multiplication and division are directly linked, so if two numbers are multiplied together to give a value, then that value divided by either of the original numbers gets you back to the other original number. Formula triangles write the multiplied values on the bottom and their product on the top. You then cover up the item you want, to find the formula for the other two items. Area of a Parallelogram = base x perp height (A = bh) Here is it’s formula triangle: If you wish to find the base, cover ‘b’… You now see that b = A/h i.e. Area divided by the perpendicular height. A b h

Trapezia A trapezium can also be made into a rectangle as shown The length of rectangle made is halfway between the length of the top of the trapezium and the length of the bottom of the trapezium (i.e. average length) The width of the new rectangle is the perpendicular height of the trapezium. top ph bottom average length perp. height perp. height

Area Formula for a Trapezium To find the average of two numbers you add them together and divide their total by 2. The average length is therefore HALF of the total of the two parallel sides added together. This average length is then multiplied by the perpendicular height. Formula: A = ½(a + b)h b a h

Quick Practice Calculate the area of this trapezium… Check by splitting the shape into a triangle on top of a rectangle… Triangle = ½ of 4 x 12 = 24 Rectangle = 11 x 12 = 132 Total = 24 + 132 = 156 P Calculate the area of this trapezium… 15cm 11cm 12.4cm 12cm Area = ½ of (15 + 11) × 12 So Area = ½ of 26 × 12 = 13 × 12 = 156cm²

What next? Finish reading through the notes, making sure you answer any questions on the areas of other quadrilaterals. Work through the MyMaths lesson and its online homework called Area of a Trapezium found at: http://app.mymaths.co.uk/271-resource/area-of-a-trapezium http://app.mymaths.co.uk/271-homework/area-of-a-trapezium Save and complete the worksheet called AreaQ-S1.xlsx Now move on to the PAV2c powerpoint