Area of shapes © T Madas.

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Presentation transcript:

Area of shapes © T Madas

Squares & Rectangles © T Madas

Area of a Square Area = length x width A = l x w w l E.g. Area = side x side A = s x s Area s s © T Madas

Area of a Square Area = length x width A = l x w E.g. A = 5 = 25 cm2 Area = side x side A = s x s Area s s E.g. © T Madas

Area of a Square Area = length x width A = l x w E.g. A = 5 = 25 cm2 Area = side x side A = s x s Area 7 cm E.g. A = 7 x 7 = 49 cm2 7 cm © T Madas

Area of a Rectangle Area = length x width A = l x w w l E.g. Area = base x height Area h A = b x h b © T Madas

Area of a Rectangle Area = length x width A = l x w E.g. A = 9 = 36 4 cm E.g. A = 9 x 4 = 36 cm2 9 cm Area = base x height Area h A = b x h b E.g. © T Madas

Area of a Rectangle Area = length x width A = l x w E.g. A = 9 = 36 4 cm E.g. A = 9 x 4 = 36 cm2 9 cm Area = base x height Area A = b x h 5 m E.g. A = 8 x 5 = 40 m2 8 m © T Madas

Composites of squares and rectangles © T Madas

Find this area A2 A1 A1= 5 x 2 = 10 cm2 2 cm A2= 2 x 3 = 6 cm2 Total Area = 16 cm2 3 cm A2 5 cm 3 cm A1 2 cm 5 cm © T Madas

– Find the area of these composite shapes 54 m2 + 8 x 8 = 64 8 64 7 3 6 54 m2 3 x 7 = 21 + 3 x 11 = 33 3 11 Lengths in metres (m) 4 4 8 x 8 = 64 8 64 8 56 m2 – 8 © T Madas

© T Madas

A2 A1 A2 A1 A1= 5 x 2 = 10 cm2 A2= 2 x 4 = 8 cm2 Total Area = 18 cm2 Perimeter = 22 cm 5 cm A1= 5 x 2 = 10 m2 4 m A2= 7 x 4 = 28 m2 5 m Total Area = 38 m2 5 m 7 m A2 2 m A1 Perimeter = 32 m 9 m © T Madas

A2 A1 A2 A1 A1= 8 x 2 = 16 cm2 A2= 7 x 3 = 21 cm2 Total Area = 37 cm2 Perimeter = 34 cm 8 cm A1= 3 x 8 = 24 m2 6 m A2= 6 x 9 = 54 m2 6 m Total Area = 78 m2 8 m 9 m A2 3 m A1 Perimeter = 46 m 14 m © T Madas

Parallelograms © T Madas

Area of a Parallelogram h Area b Area = base x height A = b x h E.g. © T Madas

Area of a Parallelogram 4 cm 7 cm Area = base x height A = b x h E.g. A = 7 x 4 = 28 cm2 © T Madas

How to draw a parallelogram 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Start with the base For example: draw a horizontal line 10 squares long © T Madas

How to draw a parallelogram Then draw a slopping line starting from one end of the bottom line. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Start with the base For example: draw a horizontal line 10 squares long © T Madas

How to draw a parallelogram Then draw a horizontal line 10 squares long Then draw a slopping line starting from one end of the bottom line. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Start with the base For example: draw a horizontal line 10 squares long © T Madas

How to draw a parallelogram Then draw a horizontal line 10 squares long Then draw a slopping line starting from one end of the bottom line. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Join the 3 sides Start with the base For example: draw a horizontal line 10 squares long © T Madas

How do we measure the height of a shape? 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 a Set Square is used to draw Right Angles The height of this parallelogram is 8 cm Line up the zero © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

What is the area of these parallelograms? 5 6 7 9 A = b x h = 7 x 5 A = b x h = 35 square units = 9 x 6 = 54 square units © T Madas

What is the area of these parallelograms? 4 6 7 4 A = b x h = 4 x 6 A = b x h = 24 square units = 7 x 4 = 28 square units © T Madas

Triangles © T Madas

Area of a Triangle A = b h b A = 2 example: h b Area of the parallelogram: A = b x h Area of the triangle: b x h A = 2 © T Madas

Area of a Triangle A = b h b A = 2 example: Area of the parallelogram: x h A = 2 4 cm 8 x 4 = 2 8 cm = 16 cm2 Area of the parallelogram: A = b x h Area of the triangle: b x h A = 2 © T Madas

Area of a Triangle another example: another example: b b A = A = 2 2 8 9 cm 6 cm 8 cm 5 cm b x h b x h A = A = 2 2 8 x 6 5 x 9 = = 2 2 = 24 cm2 = 22.5 cm2 © T Madas

Another demonstration for the area of a triangle for the formula for the area of a triangle © T Madas

Area of a Triangle A = b h b A = 2 Area of the rectangle: x h Area of triangle: b x h A = b 2 © T Madas

How do we measure the height of a shape? 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 a Set Square is used to draw Right Angles The height of this triangle is 8 cm Line up the zero © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

What is the area of these triangles? 6 7 7 8 b x h b x h A = A = 2 2 7 x 6 8 x 7 = = 2 2 = 21 square units = 28 square units © T Madas

What is the area of these triangles? 6 6 8 8 b x h b x h A = A = 2 2 8 x 6 8 x 6 = = 2 2 = 24 square units = 24 square units © T Madas

Trapezia © T Madas

Area of a Trapezium Area of the parallelogram: A = (B + b ) x h Area of the trapezium: A = 2 © T Madas

Area of a Trapezium A = (B + b ) x h 2 for example: B + b A = 2 10 + 6 56 m2 10 m A = (B + b ) x h 2 © T Madas

Area of a Trapezium A = (B + b ) x h 2 for example: B + b A = 2 15 + 7 7 cm B + b A = x h 2 8 cm 15 + 7 = x 8 2 = 88 cm2 15 cm A = (B + b ) x h 2 © T Madas

What is the area of these trapeziums? 4 10 5 6 8 6 B + b B + b A = x h A = x h 2 2 8 + 4 10 + 6 = x 5 = x 6 2 2 = 30 square units = 48 square units © T Madas

What is the area of these trapeziums? 5 4 9 6 3 9 B + b A = x h 2 B + b A = x h 9 + 5 = x 4 2 2 9 + 3 = x 6 = 28 square units 2 = 36 square units © T Madas

more demonstrations for the trapezium formula © T Madas

Area of a Trapezium (B + b ) x h A = 2 b h B b (B + b ) We changed the trapezium into a triangle with base B + b and the same height as the trapezium © T Madas

Area of a Trapezium b (B + b ) x h A = h 2 B © T Madas

more demonstrations for the trapezium formula © T Madas

Area of a Trapezium h A = (B + b ) 2 We changed the trapezium into a parallelogram with base B + b and a height, half the height of the original trapezium h A = (B + b ) x b 2 h b B (B + b ) © T Madas

Area of a Trapezium h A = (B + b ) x b 2 h B © T Madas

more demonstrations for the trapezium formula © T Madas

Area of a Trapezium [ ] b b h h B B b 2 2 B b A = + c 2 2 h A = x B 2 x h b x h 2 2 B x h b x h A = + c 2 2 h A = x [ ] B + b 2 © T Madas

more demonstrations for the trapezium formula © T Madas

Area of a Trapezium b h B B – b © T Madas

Area of a Trapezium (B – b ) x h b x h 2 [ ] b h h B – b Bh – bh A = + c 2 Bh bh A = bh + c – 2 2 bh Bh A = c + 2 2 h A = x [ ] B + b 2 © T Madas

The Area of a Kite © T Madas

Calculate the area of the following Kite 6 cm 9 cm © T Madas

Calculate the area of the following Kite 6 cm A = 9 x 3 ÷ 2 = 13.5 cm2 3 cm 9 cm Total Area = 27 cm2 is there another way to calculate the area of a kite? © T Madas

Calculate the area of the following Kite 6 cm A = 6 x 9 ÷ 2 = 27 cm2 9 cm is there another way to calculate the area of a kite? © T Madas

Areas of shapes h h s b b b h h b B A = s x s A = b 2 A = B + b 2 A = b x h A = l xw A = b x h A = b x h 2 b h h b B A = B + b 2 x h © T Madas

Revision on Areas Practice on Area © T Madas

Revision on Areas 5 cm 4 cm 30 mm 5 cm 8 cm 9 m 9 m 10 mm 5 m 4 m 7 m © T Madas

Revision on Areas 6 cm 5 cm 25 mm 6 cm 9 cm 8m 8 m 10 mm 5 m 4 m 7 m © T Madas

Revision on Areas Quick Test on Area © T Madas

Revision on Areas 5 cm 4 cm 30 mm 5 cm 8 cm 9 m 9 m 10 mm 5 m 4 m 7 m © T Madas

Revision on Areas 6 cm 5 cm 25 mm 6 cm 9 cm 8m 8 m 10 mm 5 m 4 m 7 m © T Madas

Revision on Area and Perimeter Practice on Area & Perimeter © T Madas

Revision on Area and Perimeter A = 24 m2 A = 40 m2 A = 16 m2 P = 22 m P = 32 m P = 22 m 4 m 12 mm 7 cm 12 cm 10 cm 9 mm 8 mm 6 cm 6 cm 10 mm 8 cm 8 cm A = 40mm2 A = 24 cm2 A = 24 cm2 P = 31mm P = 27 cm © T Madas P = 24 cm

Revision on Area and Perimeter 5 cm 6 cm 5 m 4 cm 5 cm 11 m 3 m 5 m 7 m 9 cm 5 m A = 21 m2 A = 28 cm2 A = 25 m2 P = 24 m P = 25 cm P = 32 m 15 mm 13 mm 15 cm 9 mm 7 mm 16 mm 9 cm 10 mm 12 mm 29 mm 12 cm A = 42mm2 A = 54 cm2 A = 220 mm2 P = 34mm P = 36 cm P = 70 mm © T Madas

Revision on Area and Perimeter 5 cm 12 mm 9 mm 8 mm 8 m 6 cm 4 cm 5 cm 10 m 10 m 8 m 10 mm 9 cm A = 40mm2 A = 96 m2 A = 28 cm2 P = 44 m P = 31mm P = 25 cm 15 mm 15 m 10 cm 16 mm 6 cm 10 m 8 m 11 m 10 mm 8 cm 29 mm 35 m A = 24 cm2 A = 220 mm2 A = 200 m2 P = 24 cm P = 70 mm P = 71 m © T Madas

Revision on Area and Perimeter Quick Test Area & Perimeter © T Madas

Revision on Area and Perimeter A = 24 m2 A = 40 m2 A = 16 m2 P = 22 m P = 32 m P = 22 m 4 m 12 mm 7 cm 12 cm 10 cm 9 mm 8 mm 6 cm 6 cm 10 mm 8 cm 8 cm A = 40mm2 A = 24 cm2 A = 24 cm2 P = 31mm P = 27 cm © T Madas P = 24 cm

Revision on Area and Perimeter 5 cm 6 cm 5 m 4 cm 5 cm 11 m 3 m 5 m 7 m 9 cm 5 m A = 21 m2 A = 28 cm2 A = 25 m2 P = 24 m P = 25 cm P = 32 m 15 mm 13 mm 15 cm 9 mm 7 mm 16 mm 9 cm 10 mm 12 mm 29 mm 12 cm A = 42mm2 A = 54 cm2 A = 220 mm2 P = 34mm P = 36 cm P = 70 mm © T Madas

Revision on Area and Perimeter 5 cm 12 mm 9 mm 8 mm 8 m 6 cm 4 cm 5 cm 10 m 10 m 8 m 10 mm 9 cm A = 40mm2 A = 96 m2 A = 28 cm2 P = 44 m P = 31mm P = 25 cm 15 mm 15 m 10 cm 16 mm 6 cm 10 m 8 m 11 m 10 mm 8 cm 29 mm 35 m A = 24 cm2 A = 220 mm2 A = 200 m2 P = 24 cm P = 70 mm P = 71 m © T Madas

Missing Lengths Missing Lengths © T Madas

Missing Lengths ? ? ? ? ? ? 4 m 4 m 10 m 6 m 4 m 4 m 8 mm 6 cm 5 cm A = 40 m2 A = 24 m2 A = 16 m2 4 m 4 m ? ? 6 m 10 m 4 m ? A = 40mm2 4 m A = 24 cm2 A = 20 cm2 8 mm ? 6 cm 5 cm 10 mm 8 cm ? 8 cm ? © T Madas

Missing Lengths ? ? ? ? ? ? 9 m 7 m 12 m 9 m 9 m 5 m 6 mm 4 cm 6 cm A = 60 m2 A = 63 m2 A = 81 m2 7 m 9 m ? ? 9 m 12 m 9 m ? A = 30mm2 5 m A = 10 cm2 A = 24 cm2 6 mm ? 4 cm 6 cm 10 mm 5 cm ? 8 cm ? © T Madas

Missing Lengths Missing Lengths [quick test] © T Madas

Missing Lengths ? ? ? ? ? ? 4 m 4 m 10 m 6 m 4 m 4 m 8 mm 6 cm 5 cm A = 40 m2 A = 24 m2 A = 16 m2 4 m 4 m ? ? 6 m 10 m 4 m ? A = 40mm2 4 m A = 24 cm2 A = 20 cm2 8 mm ? 6 cm 5 cm 10 mm 8 cm ? 8 cm ? © T Madas

Missing Lengths ? ? ? ? ? ? 9 m 7 m 12 m 9 m 9 m 5 m 6 mm 4 cm 6 cm A = 60 m2 A = 63 m2 A = 81 m2 7 m 9 m ? ? 9 m 12 m 9 m ? A = 30mm2 5 m A = 10 cm2 A = 24 cm2 6 mm ? 4 cm 6 cm 10 mm 5 cm ? 8 cm ? © T Madas

Areas on a Grid © T Madas

35 54 45 64 What is the area of these parallelograms? 5 6 7 9 5 8 9 8 © T Madas

36 60 35 56 What is the area of these parallelograms? 6 6 6 10 5 8 7 7 © T Madas

25 28 24 35 What is the area of these parallelograms? 4 7 5 5 5 6 7 4 © T Madas

30 55 63 49 What is the area of these parallelograms? 5 5 6 11 7 9 7 7 © T Madas

30 56 20 42 What is the area of these parallelograms? 8 7 5 6 6 5 7 4 © T Madas

21 27 25 32 What is the area of these triangles? 6 6 7 9 5 8 10 8 © T Madas

18 30 35 28 What is the area of these triangles? 6 6 6 10 5 8 14 7 © T Madas

14 20 35 12 What is the area of these triangles? 4 7 5 8 10 6 7 4 © T Madas

15 30 24.5 31.5 What is the area of these triangles? 5 5 6 12 7 9 7 7 © T Madas

28 15 21 10 What is the area of these triangles? 8 7 5 6 6 7 5 4 © T Madas

35 45 30 60 What is the area of these trapeziums? 4 8 5 5 10 10 9 8 5 12 © T Madas

48 63 36 40 What is the area of these trapeziums? 5 6 9 10 4 11 12 3 4 17 © T Madas

45 60 34 28 What is the area of these trapeziums? 4 6 8 10 5 11 12 9 4 © T Madas

Quick Test on Areas on a Grid © T Madas

35 54 45 64 What is the area of these parallelograms? 5 6 7 9 5 8 9 8 © T Madas

36 60 35 56 What is the area of these parallelograms? 6 6 6 10 5 8 7 7 © T Madas

25 28 24 35 What is the area of these parallelograms? 4 7 5 5 5 6 7 4 © T Madas

30 55 63 49 What is the area of these parallelograms? 5 5 6 11 7 9 7 7 © T Madas

30 56 20 42 What is the area of these parallelograms? 8 7 5 6 6 5 7 4 © T Madas

21 27 25 32 What is the area of these triangles? 6 6 7 9 5 8 10 8 © T Madas

18 30 35 28 What is the area of these triangles? 6 6 6 10 5 8 14 7 © T Madas

14 20 35 12 What is the area of these triangles? 4 7 5 8 10 6 7 4 © T Madas

15 30 24.5 31.5 What is the area of these triangles? 5 5 6 12 7 9 7 7 © T Madas

28 15 21 10 What is the area of these triangles? 8 7 5 6 6 7 5 4 © T Madas

35 27 45 32 What is the area of these shapes? 5 6 7 9 5 8 9 8 © T Madas

60 18 56 35 What is the area of these shapes? 6 6 10 6 5 8 14 7 © T Madas

36 30 35 28 What is the area of these shapes? 6 6 6 10 5 8 7 7 © T Madas

54 21 64 25 What is the area of these shapes? 6 6 9 7 5 8 10 8 © T Madas

25 14 24 35 What is the area of these shapes? 4 7 5 5 10 6 7 4 © T Madas

30 28 20 21 What is the area of these shapes? 8 7 5 6 6 7 5 4 © T Madas

28 20 35 12 What is the area of these shapes? 4 7 5 8 5 6 7 4 © T Madas

30 30 63 24.5 What is the area of these shapes? 5 5 6 12 7 9 7 7 © T Madas

55 15 49 31.5 What is the area of these shapes? 5 5 6 11 7 9 7 7 © T Madas 7

56 15 42 10 What is the area of these shapes? 8 7 5 6 6 7 5 4 © T Madas

35 45 30 60 What is the area of these trapeziums? 4 8 5 5 10 10 9 8 5 12 © T Madas

48 63 36 40 What is the area of these trapeziums? 5 6 9 10 4 11 12 3 4 17 © T Madas

45 60 34 28 What is the area of these trapeziums? 4 6 8 10 5 11 12 9 4 © T Madas

© T Madas