areaofshapes_tcm4-123387

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What Is Area ? :

What Is Area ? Area is the amount of space inside a shape: Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area is measured in square centimetres. A square centimetre is a square measuring one centimetre in each direction. It is written as :

Estimating The Area. :

Estimating The Area. Look at the four shapes below and use your judgement to order them from smallest to largest area:

Slide 3:

To decide the order of areas consider the four shapes again: To measure the area we must determine how many square centimetres are in each shape: Each shape is covered by 36 squares measuring a centimetre by a centimetre .We can now see that all the areas are equal at 36cm2 each.

Area Of A Rectangle. :

Area Of A Rectangle. Look again at one of the shapes whose area we estimated: What was the length of the rectangle ? 9cm How many rows of 9 squares can the breadth hold ? 4 We can now see that the area of the rectangle is given by 9 x 4. The formula for the area of a rectangle is: Area = Length x Breadth or

Slide 5:

We can now calculate the area of each rectangle very quickly: A= L x B A = 6 x 6 =36cm2 A= L x B A = 12 x 3 =36cm2 A= L x B A = 9 x 4 =36cm2 A= L x B A = 18 x 2 =36cm2

Slide 6:

Example 1 Calculate the area of the rectangle below: Solution A = LB L = 7 B = 4 A = 7 x 4 A = 28cm2 This area is in square metres: Solution A = LB L = 3 B = 5 A = 3 x 5 A = 15m2

What Goes In The Box ? :

What Goes In The Box ? Find the area of the shapes below : 48cm2 11.34m2

The Area Of A Triangle. :

The Area Of A Triangle. Consider the right angled triangle below: What shape is the triangle half of ? Rectangle What is the area of the rectangle? Area = 8 x 5 = 40 cm2 What is the area of the triangle ? Area = ½ x 40 = 20cm2 The formula for the area of a triangle is: Area = ½ x Base x Height A = ½ BH

Slide 9:

Does the formula apply to all triangles ? Can we make this triangle into a rectangle ? Yes The triangle is half the area of this rectangle: The areas marked A1 are equal. The areas marked A2 are equal. For all triangles: Area = ½ BH

Slide 10:

Calculate the areas of the triangles below: Example 1 Solution. Area = ½ x base x height base = 10 cm height = 6cm Area = ½ x 10 x 6 Area = ½ x 60 = 30cm2 Example 2 Solution. Area = ½ x base x height base = 6.4m height = 3.2m Area = ½ x 6.4 x 3.2 Area = ½ x 20.48 = 10.24m2

The Area Of A Circle. :

The Area Of A Circle. Consider the circle below divided into quarters: We are going to place the quarters as shown to make the shape below We can fit a rectangle around this shape: At the moment it is hard to see why this should tell us how to calculate the area of a circle.

Slide 12:

Now consider the same circle split into eight parts: The eight parts are arranged into the same pattern as last time: This time the shapes fit the rectangle more closely:

Slide 13:

This time the shapes fit the rectangle more closely: What length must the breadth B be close to ? B = r What length must the length L be close to ? Half of the circumference of the circle. If C = 2  r then L =  r . We now have an approximate length and breadth of our rectangle.

 r . :

 r . What is the area of the rectangle ? A =  r x r A =  r 2 If the circle was split into more and more smaller segments and the segments arranged in the same pattern, then the parts would become the rectangle shown above. See “Autograph Extras”, “New”, “Area Of Circle” for further info’.

Slide 15:

Find the area of the circles below: Example 1. A =  r 2 r = 10 A = 3.14 x 10 x 10 A = 314 cm2 Example 2 A =  r 2 r = 1.35m A = 3.14 x 1.35 x 1.35 A = 5.72m2 ( to 2 d.p)

What Goes In The Box ? 4 :

What Goes In The Box ? 4 Find the area of the shapes below : 153.86cm2 31.16m2 ( 2 d.p) 