Perimeter & Area

Area of Shapes The area of a shape is the space it occupies. Try guessing the name of these shapes first: Square Rectangle ParallelogramTrapezium Circle Triangle

The Square Area = l x b l b e.g. Find the area of a square of side 3.5 cm. Discuss and work out this example together with your friend. A = l x b A = 3.5 cm x 3.5 cm = cm 2

The Rectangle Area = l x b l b e.g. Find the area of a rectangle of length 3.5 cm and height 80 mm. Discuss and work out this example together. Since units must be the same: 10 mm = 1 cm 80 mm = 80 mm ÷ 10 = 8 cm A = l x b A = 3.5 cm x 8 cm = 28 cm 2

The Parallellogram Area = b x h baseb heighth b h e.g. Find the area of a parallelogram correct to 1 d.p. 3.8 cm 10.3 cm Discuss and work out this example together. A = b x h A = 10.3 cm x 3.8 cm = cm 2 = 39.1 cm 2

The Triangle Area = ½ b  h e.g. Find the area of triangle ABC correct to the nearest cm 2. Discuss and work out this example together. A = ½b x h A = ½ x 4 cm x 11.7 cm = 23.4 cm 2 = 23 cm 2 baseb heighth Area of parallelogram = b  h b h Area of = ½ area of parallelogram b h 11.7 cm 4 cm A BC Area of = ½b  h b h

b  Area of trapezium = ½ h(a + b) Rotate the trapezium The 2 trapeziums form a parallelogram Area of parallelogram = h(a + b) Area of 1 trapezium is half h(a + b) Area = ½h(a + b) a b h h a e.g. Find the area of the trapezium. 12 cm 8.5 cm 6 cm Decide about the values of a, b and h to find the area. h = 6cm, a = 8.5 cm, b = 12 cm A = ½h(a + b) A = ½ x 6 cm x (8.5 cm + 12 cm) = ½ x 6 cm x 20.5 cm = 61.5 cm 2 The Trapezium Length of side a Length of side b Copy the trapezium a b height

The Circle Area =  r 2 Centre Radius r Remember: the radius of a circle is half the diameter. e.g. The diameter of a circle is 19 cm. Find, correct to nearest whole number, the area of a circle. Find the radius first and then work out this example together. r = 19 cm ÷ 2 = 9.5 cm. A =  r 2 =  x 9.5 cm x 9.5 cm = cm 2 = 284 cm 2

Answers: 6a) $1.92 6b) $2.70 6c) $3.08 6d) $1.00 6e) H

Find the perimeters of the following:

Find the perimeter of the following:

Areas: Defines the size of an enclosed space, by calculating the number of square units of a certain size which are needed to cover the surface of a figure. Hence why area is measured in units squared. E.g. the area of the shape below is 8 units 2

Areas of plane shapes:

Answers: 9) cm 2 10) cm 2 11) 55 m 2 12) 15 m 2 13) 3.64 m (2dp) 14) roses = 16 m 2, azaleas 28 m 2, vegetables = 40 m 2, total = 84 m 2 15a ) i) m 2, ii) 1395 m 2, iii) 1215 m 2, iv) 1750m 2 15b) Trapezium, c) i) m 2, d) ii) ha

Proof of Area rule of a Trapezium Start with Trapezium of height h, with lengths a and b Split trapezium up into 2 triangles and 1 rectangle. Find the area of the individual components.

Find the area of the following trapezium.

Find the ratio Draw 5 – 10 circles, starting off with circles with a small radius, moving up to those with a larger radius. Measure the circumference (piece of string?) and diameter of each circle. Find the ratio between the circumference and diameter of a circle.

Starter Q1) Q2) a) b) c) d)

answers 1) 25m 2 larger 2a) 50m 2 2b) 5cm, because it is the depth 3c) 1700

Starter 1300