Area

MeasurementsMeasurements

Limits of accuracyLimits of accuracy

The accuracy of a measurement is The accuracy of a measurement is how close that measurement is to how close that measurement is to the true value. the true value.

This is restricted or limited by the This is restricted or limited by the accuracy of the measuring accuracy of the measuring instrument.instrument.

The ruler is marked in The ruler is marked in centimetres, so any length centimetres, so any length measured with it can only be given measured with it can only be given to the nearest centimetre.to the nearest centimetre.

Limit of AccuracyLimit of Accuracy For each of these measuring scales, For each of these measuring scales,

state the size of one unit on the scale state the size of one unit on the scale and state the limit of accuracy.and state the limit of accuracy.

(a)(a) The size of one unit is 1 kg. The limits The size of one unit is 1 kg. The limits of accuracy are ±0.5 × 1 kg = ±0.5 kg.of accuracy are ±0.5 × 1 kg = ±0.5 kg.

(b)(b) The size of one unit is 5 mL. The limits The size of one unit is 5 mL. The limits of accuracy are ±0.5 × 5 mL = ±2.5 mL.of accuracy are ±0.5 × 5 mL = ±2.5 mL.

AreaArea

The Area of a Shape is the The Area of a Shape is the Amount of Surface that is Amount of Surface that is Enclosed by the shapeEnclosed by the shape

AreaArea Can use grid paper to determine size of Can use grid paper to determine size of

areaarea

Area = 4cmArea = 4cm22

Area = 3 squares + ½ Area = 3 squares + ½

square + ½ squaresquare + ½ square = 4 cm = 4 cm 22

Converting units of areaConverting units of area 1 cm = 10 mm1 cm = 10 mm 1 cm1 cm22 = 10 × 10 mm = 10 × 10 mm22 = 100 mm = 100 mm22

(double the number of zeros)(double the number of zeros)

1 m = 100 cm1 m = 100 cm 1 m1 m22 = 100 × 100 cm = 100 × 100 cm22 = 10 000 cm = 10 000 cm22


1 m = 1000 mm1 m = 1000 mm 1 m1 m22 = 1000 × 1000 mm = 1 000 000 mm = 1000 × 1000 mm = 1 000 000 mm22


Conversions of UnitsConversions of Units

1cm1cm22 = 100mm = 100mm22

1m1m22 = 10 000cm = 10 000cm22

1m1m22 = 1 000 000mm = 1 000 000mm22

Investigation of Area of Investigation of Area of TrianglesTriangles

Area of right-angled trianglesArea of right-angled triangles You will need 1-cm grid paper.You will need 1-cm grid paper. a On your grid paper, draw a rectangle 6 cm a On your grid paper, draw a rectangle 6 cm

by 4 cm.by 4 cm. b Cut the rectangle in half along a diagonal. b Cut the rectangle in half along a diagonal.

What shape have you made?What shape have you made? c Area of rectangle = ×c Area of rectangle = ×

= cm2= cm2 d What is the area of each triangle?d What is the area of each triangle?

What do you notice regarding the area of What do you notice regarding the area of the triangle and the area of the rectangle?the triangle and the area of the rectangle?

Area of squares, rectangles Area of squares, rectangles and trianglesand triangles

Area of square = side × sideArea of square = side × side = = s s × × ss = = ss22

Area of rectangle = length × breadthArea of rectangle = length × breadth = = l l × × bb

Area of triangle = ½ × base × heightArea of triangle = ½ × base × height = ½ × = ½ × b b × × hh

ExamplesExamples 1 What is the area of this square?1 What is the area of this square? SolutionSolution Area = Area = s s × × ss = 3.2 × 3.2= 3.2 × 3.2 = 1024 cm= 1024 cm22

2 What is the area of this rectangle?2 What is the area of this rectangle? SolutionSolution Area = Area = l l × × b b 6 cm = 60 mm6 cm = 60 mm = 60 × 5= 60 × 5 = 300 mm2= 300 mm2

Area of a TriangleArea of a Triangle 1 Find the area of this triangle.1 Find the area of this triangle. SolutionSolution Area of triangle = ½ × Area of triangle = ½ × b b × × hh = ½ × 8 × 6= ½ × 8 × 6 = 24 m= 24 m22

Note: Note: The length of 7 m was not required to The length of 7 m was not required to find this triangle’s area.find this triangle’s area.

2 Find the area of this triangle.2 Find the area of this triangle. SolutionSolution Area of triangle = ½ × Area of triangle = ½ × b b × × hh = ½ × 4.2 × 3= ½ × 4.2 × 3 = 6.3 cm= 6.3 cm22

Areas of composite shapesAreas of composite shapes

Find the area of this shape.Find the area of this shape. SolutionSolution Method 1Method 1 Area of shape = area of rectangle Area of shape = area of rectangle

Y + area of square XY + area of square X = (6 × 2) + (3 × 3)= (6 × 2) + (3 × 3) = 12 + 9= 12 + 9 = 21 cm= 21 cm22

Method 2Method 2 This can also be done by This can also be done by

subtracting areas.subtracting areas. Area of shape = area of Area of shape = area of

rectangle S − area of square rectangle S − area of square RR

= 6 × 5 − 3 × 3= 6 × 5 − 3 × 3 = 30 − 9= 30 − 9 = 21 cm= 21 cm22

What about this shaded What about this shaded area?area?

Area of purple shape = area of big Area of purple shape = area of big rectangle − area of small rectanglerectangle − area of small rectangle

= (75 × 45) − (32 × 24)= (75 × 45) − (32 × 24) = 3375 − 768= 3375 − 768 = 2607 mm= 2607 mm22

What shapes can you see?What shapes can you see?

SolutionSolution Divide the shape into a Divide the shape into a

triangle and a rectangle.triangle and a rectangle. Area of shape = area of rectangle + Area of shape = area of rectangle +

area of trianglearea of triangle = (16 × 14) + (½ × 14 × 14)= (16 × 14) + (½ × 14 × 14) = 224 + 98= 224 + 98 = 322 cm= 322 cm22

224cm2

A = ½bh98cm2

Measuring Large AreasMeasuring Large Areas 1 hectare is about the size of 2 football 1 hectare is about the size of 2 football

fieldsfields 1 hectare 1 hectare = = (100 (100 × × 100) m100) m22

1 ha 1 ha = = 10 000 m10 000 m22

1 square kilometre is a square 1km by 1 square kilometre is a square 1km by 1km1km

1 km2 1 km2 = = 1000m x 1000m1000m x 1000m = = 1 000 000 m1 000 000 m22

= 100 hectares (ha)= 100 hectares (ha)

A nature reserve has an area of 9 577 000 000 m2.A nature reserve has an area of 9 577 000 000 m2. a What is its area in hectares? b What is its area in a What is its area in hectares? b What is its area in

square kilometres?square kilometres?

SolutionSolution a Area of reserve = 9 577 000 000 ma Area of reserve = 9 577 000 000 m22 (1ha = (1ha =

10000m10000m22)) = (9 577 000 000 ÷ 10 000) ha= (9 577 000 000 ÷ 10 000) ha = 957 700 ha= 957 700 ha

The area of the reserve is 957 700 hectares.The area of the reserve is 957 700 hectares.

b Area of reserve = 9 577 000 000 m2 (1 kmb Area of reserve = 9 577 000 000 m2 (1 km2 = 2 = 1 000 1 000 000m000m22))

= (9 577 000 000 ÷ 1 000 000) km2= (9 577 000 000 ÷ 1 000 000) km2 = 9577 km= 9577 km22

The area of the reserve is 9577 square kilometres.The area of the reserve is 9577 square kilometres.

Area

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