Grade 6 / areas 30 exercises (including 28 corrected)

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Fig.1Fig.2Fig.3 F1F2F3 F4F5F6 1uaS1S2 S1S2S31ua 1. Comparison of the surface E.5581 Of the two figures below, which one has the larger area: 2. Differentiate between perimeter and area E.1686 Consider the three figures below : 1 Compare the perimeters of each of these figures. 2 Compare the areas of each of these figures. E.5758 Below are six figures constructed from a rectangle whose length measures twice the width and half disks (remove or add) whose diameter is the width of the rectangle: 1 a Are there any figures that possess the same perime-ter? b Which figure has the largest perimeter? 2 a Are there any figures with the same area? b Which figure has the largest area? 3. Areas by tiling E.10519 Consider the two shaded quadrilat-erals shown below in a grid. We’ll use a small square of this grid as the unit of area ( 1 u . a . ) . 1 Measure the two surfaces S 1 and S 2 in units of area. 2 Recall the formulas for determining the areas of rectan-gles and squares. E.11126 Consider the three shaded polygons shown below in a grid. We will use a small square of this grid as a unit of area ( 1 u . a . ) and its sides will represent the unit of length. Complete the table below : S 1 S 2 S 3 Perimeter Area https://chingmath.fr chapExoCorrec/5581 sacados/5581 chapExoCorrec/1686 sacados/1686 Fig.1Fig.2Fig.3 chapExoCorrec/5758 sacados/5758 F1F2F3 F4F5F6 chapExoCorrec/10519 sacados/10519 1uaS1S2 chapExoCorrec/11126 sacados/11126 S1S2S31ua
1uaS1S2 1u.a BCA 1cm1cm E.5588 Consider the two shaded polygons shown below in a grid. We will use a small square of this grid as a unit of area ( 1 u . a . ) . 1 Measure the two areas S 1 and S 2 in units of area. 2 Compare the area of the two shaded polygons. E.1697 In this exercise, we measure areas using the squares that form the figure’s grid. 1 Justify that the area of the right-angled triangle is 6 squares. 2 Determine the area of the kite on the right. E.2595 Determine the areas of the three figures below : 4. Area units E.978 Consider the grid below, showing four hatched rectangles. 1 For each grid, give the fraction representing the hatched part relative to the square of side 1 cm . 2 Give the decimal form of each of the fractions obtained in the previous question. E.2606 Each drawing below represents a square with a side of one centimetre. Its area is therefore one square centimetre. The grid lines shown are spaced one millimetre apart. In each case, cross-hatch the part of the square centimetre: a 1 100 cm 2 b 1 10 cm 2 c 0.24 cm 2 d 0.05 cm 2 e 0.99 cm 2 https://chingmath.fr chapExoCorrec/5588 sacados/5588 1uaS1S2 chapExoCorrec/1697 sacados/1697 1u.a chapExoCorrec/2595 sacados/2595 BCA chapExoCorrec/978 sacados/978 1cm1cm chapExoCorrec/2606 sacados/2606
ABC1cm2 ABCD1cm21mm2 E.2507 Three rectangles are shown in the grid below : Copy and complete the table below Longueur (en cm ) Largeur (en cm ) Périmètre (en cm ) Aire (en cm 2 ) A B C E.1693 The figure below shows the surface defined by: 1 cm 2 : this is the area of a square of one centimeter side. 1 mm 2 : this is the area of a square one millimeter on a side. Complete the table below by indicating the area of the four figures shown with the two units of measurement : A B C D Area in cm 2 Area in mm 2 E.2607 Use the millimetre paper below to obtain figures with the required area: a The figure A has area 3.04 cm 2 . b The figure B has area 2.2 cm 2 . c Figure C has area 2.51 cm 2 . 5. Areas of rectangles https://chingmath.fr chapExoCorrec/2507 sacados/2507 ABC1cm2 chapExoCorrec/1693 sacados/1693 ABCD1cm21mm2 chapExoCorrec/2607 sacados/2607
ABCD5cm3cmEFGH4cm2cm ABCDEFG3cm4cm2cm1cm E.7930 Proposition: For a rectangle of length L and width ‘ : The perimeter P of the rectangle has the value : P = 2 × L + ‘ (or P =2 × L +2 × ‘ ) The area A of the rectangle has the value : A = L × ‘ Consider the two rectangles ABCD and EFGH shown be-low : Determine the perimeters and areas of these two rectangles. E.11096 The figure below is composed of two rectangles : 1 Justify that the rectangle DEFG has width 3 cm . 2 a Determine the perimeter of this figure. b Determine the area of this figure. E.1687 Each column represents information on a rectangle. Complete this table in full, also marking the operations per-formed. Rectangle 1 Rectangle 2 Rectangle 3 Longueur 40 m 100 m Largeur 15 m 20 m Périmètre 300 m Aire 700 m 2 6. Area Conversions: All About Square Meters E.11762 Recopier et effectuer les conversions suiv-antes : a 54 m 2 = : : : : : : dm 2 b 0 ; 17 m 2 = : : : : : : cm 2 c 1 ; 07 m 2 = : : : : : : dm 2 d 0 ; 904 m 2 = : : : : : : cm 2 E.11763 Recopier et effectuer les conversions suiv-antes : a 54 dm 2 = : : : : : : m 2 b 184 cm 2 = : : : : : : m 2 c 9 dm 2 = : : : : : : m 2 d 1054 cm 2 = : : : : : : m 2 7. Area conversions E.1700 In the table below, for each line, take the area value shown on the left and convert it to the unit shown on the right : km 2 hm 2 dam 2 m 2 dm 2 cm 2 mm 2 22 cm 2 mm 2 54.7 m 2 hm 2 57 m 2 dam 2 7541 dam 2 km 2 0.0451 km 2 m 2 E.1691 Copy and perform the following con-versions : a 450 m 2 = : : : : : : dam 2 b 35.1 cm 2 = : : : : : : dm 2 c 6.12 dm 2 = : : : : : : dam 2 d 6.5 hm 2 = : : : : : : m 2 e 0.003 5 km 2 = : : : : : : m 2 f 354 dm 2 = : : : : : : dam 2 E.1692 Copy and perform the following con-versions : a 56 830 cm 2 = : : : : : : m 2 b 7 dam 2 = : : : : : : m 2 c 46 000 m 2 = : : : : : : km 2 d 3.5 km 2 = : : : : : : m 2 e 3 m 2 = : : : : : : cm 2 f 0.0071 km 2 = : : : : : : m 2 g 0.68 cm 2 = : : : : : : mm 2 h 1.8 km 2 = : : : : : : hm 2 https://chingmath.fr chapExoCorrec/7930 sacados/7930 ABCD5cm3cmEFGH4cm2cm chapExoCorrec/11096 sacados/11096 ABCDEFG3cm4cm2cm1cm chapExoCorrec/1687 sacados/1687 sacados/11762 sacados/11763 chapExoCorrec/1700 sacados/1700 chapExoCorrec/1691 sacados/1691 chapExoCorrec/1692 sacados/1692
E.4229 Copy and perform the following con-versions : a 1 200 cm 2 = : : : : : : dam 2 b 0.045 km 2 = : : : : : : dam 2 c 2 dm 2 = : : : : : : mm 2 d 75.2 dam 2 = : : : : : : m 2 e 0.004 75 hm 2 = : : : : : : m 2 f 35 dm 2 = : : : : : : hm 2 E.11097 Copy and complete the missing dotted lines : a 42.5 cm 2 = : : : dm 2 b 0.045 km 2 = : : : dam 2 c 0.48 m 2 = : : : cm 2 d 450 mm 2 = : : : m 2 E.11127 Copy and fill in the missing dotted lines : a 0.425 hm 2 = : : : m 2 b 145 m 2 = : : : dam 2 c 9.7 cm 2 = : : : dm 2 d 4.8 dam 2 = : : : dm 2 E.1698 Copy and fill in the missing dotted lines. a 15 m 2 = 1500 : : : b 1.3001 dam 2 = 1 300 100 : : : c 0.0057 m 2 = 57 : : : : : : d 27.3 hm 2 = 0.273 : : : : : : E.1699 Below are area measurements ex-pressed in various units ; add these areas together and convert the result to the requested unit. a 3 hm 2 51 dam 2 = : : : : : : km 2 b 3 dam 2 5 dm 2 312 cm 2 = : : : : : : m 2 8. Area conversions and measurements in ares E.9994 Copy and complete the missing blanks. a 5 a = : : : : : : m 2 b 450 m 2 = : : : : : : a c 13 ha = : : : : : : a d 25.1 a = : : : : : : ha 9. Problems E.2636 An inhabitant of Douala in Cameroon has just bought a villa whose garden has the shape of a rectangle of 35 m length and 20 m width. He plans to build a small swimming pool whose dimensions are 12 m long and 8 m wide ; lawn will be laid on the rest of the garden. 1 Determine the area of the pool. 2 Determine the area occupied by the lawn. E.1695 A person purchases a plot of 600 m 2 . Elle veut construire une maison rectangulaire de 12 m sur 7.8 m , mais pour avoir le droit de construire, la surface de la maison ne doit pas dépasser les 2 10 de la surface du terrain. 1 What is the areaof the house? 2 Will this person have the right to build his house? 10. Unclassified exercises E.1222 1 Draw the triangle ABC such that : AB = 8 cm ; BAC = 30 o ; ABC = 50 o 2 Draw the perpendicular bisector of segment [ AC ] 3 Tracer la hauteur issue de C https://chingmath.fr chapExoCorrec/4229 sacados/4229 chapExoCorrec/11097 sacados/11097 chapExoCorrec/11127 sacados/11127 chapExoCorrec/1698 sacados/1698 chapExoCorrec/1699 sacados/1699 chapExoCorrec/9994 sacados/9994 chapExoCorrec/2636 sacados/2636 chapExoCorrec/1695 sacados/1695 chapExoCorrec/1222 sacados/1222