smc-666-20-Area

Measurement, NAP-H3-CA06

What shape has an area greater than 3 square units

`text(A)`	`text(B)`	`text(C)`	`text(D)`

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`C`

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`text(Consider triangle)\ C:`

`text(Area)`	`=1/2 xx b xxh`
	`=1/2 xx 3 xx3`
	`=4.5\ text(square units)`

`=>C`

Measurement, NAP-J3-CA11

A triangle is drawn on grid paper.

What is the area of the triangle?

6 squares	8 squares	12 squares	16 squares

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`text(8 squares)`

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`text(Area)`	`= 1/2 xx text(base) xx text(height)`
	`= 1/2 xx 4 xx 4`
	`= 8\ text(squares)`

Measurement, NAP-B3-CA09

A resort has 4 pools.

Which pool has the largest surface area?

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`text(Consider the surface area of each pool:)`

`text(1st pool) = 6 xx 19 = 114`

`text(2nd pool) = 7 xx 18 = 126`

`text(3rd pool) = 12.5 xx 12.5 = 156.25`

`text(4th pool) =10 xx 15 = 150`

`:.\ text(The 3rd pool, 12.5 × 12.5, has the largest)`

`text(surface area.)`

Measurement, NAP-D3-CA29 SA

Poppy draws a quadrilateral with a perimeter of 50 centimetres.

What is the maximum possible area of Poppy's quadrilateral?

square centimetres

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`156.25\ text(cm²)`

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`text(The maximum area will occur when the)`

`text(quadrilateral is a square.)`

`=>\ text(Length of side) = 50/4 = 12.5\ text(cm)`

`:.\ text(Maximum area)`	`= 12.5 xx 12.5`
	`= 156.25\ text(cm²)`

Measurement, NAP-D3-NC08

Bob had a mini tennis court in his backyard, as shown in the diagram below.

What is the area of the mini tennis court?

	`6\ text(square metres)`
	`12\ text(square metres)`
	`24\ text(square metres)`
	`48\ text(square metres)`

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`24\ text(m²)`

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`text(The mini tennis court has dimensions)`

`4 xx 6.`

`:.\ text(Area)`	`= 4 xx 6`
	`= 24\ text(m²)`

Measurement, NAP-E3-CA03

A neighbourhood soccer oval is marked out with the dimensions shown below.

What is the area of the field?

	`298\ text(square metres)`
	`2842.75\ text(square metres)`
	`5261.25\ text(square metres)`
	`8123.25\ text(square metres)`

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`5261.25\ text(m²)`

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`text(Area of the soccer field)`

`= 57.5 xx 91.5`

`= 5261.25\ text(m²)`

Measurement, NAP-E3-NC31 SA

This triangle was made by cutting a square in half.

The perimeter of the triangle is 51.21 cm.

What is the area of the triangle?

square centimetres

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`112.5\ text(cm²)`

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`text{Triangle is isosceles (half a square).}`

`=>\ text(Length of triangle side)`

`= 1/2 xx (51.21 – 21.21)`

`= 1/2 xx 30`

`= 15\ text(cm)`

`:.\ text(Area)`	`= 1/2 bh`
	`= 1/2 xx 15 xx 15`
	`= 112.5\ text(cm²)`

Measurement, NAP-F3-CA32 SA

A square has an area of 169 square centimetres.

What is the perimeter?

centimetres

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`52`

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`text(Let)\ \ x = text(length of 1 side)`

`text(Area) = x xx x`	`= 169`
`x^2`	`= 169`
`x`	`= sqrt 169`
	`= 13\ text(cm)`

`:.\ text(Perimeter)`	`= 4 xx 13`
	`= 52\ text(cm)`

Measurement, NAP-B3-NC09 SA

The area of the shaded rectangle below is 84 cm².

What is the length of the shaded rectangle?

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`14`

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`text(Let)\ \ d =\ text(length of rectangle)`

`d xx 6`	`=84`
`:. d`	`=84/6`
	`=14\ text(cm)`

Measurement, NAP-C3-CA28 SA

Tom decided to cover a rectangular floor with tiles.

The tiles are twice as wide as they are long.

The floor is `5 1/2` tiles wide and `11 1/2` tiles long.

Using this pattern, what is the total number of tiles Tom will use to cover the floor?

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`226.5\ \ text(tiles)`

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`text(Strategy 1:)`

`text(Tiles in bottom row =)\ 11 1/2`

`text(Tiles in top rows)`	`=5 xx 23`
	`=115`

`:.\ text(Total tiles) = 115 + 11.5 = 126.5`

`text(Strategy 2:)`

`text(Let)\ \ x= text(length of 1 tile)`

`=>\ text(Area of 1 tile)\ = 1 xx 1/2 = 1/2\ text(u²)`

`text{Area of the floor}`	`= 5 1/2 xx 11 1/2`
	`=63.25\ text(u²)`

`:.\ text(Total tiles )`	`=63.25/0.5`
	`=126.5\ text(tiles)`

Geometry, NAP-C3-CA26 SA

Jill is playing in her parents' rectangular courtyard.

The courtyard is measured at 6m by 10m.

Jill draws a triangle on the courtyard with chalk, pictured below.

What is the area of this triangle?

The triangle is

square metres

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`14\ text(m²)`

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`text(Area of)\ Delta`	`= 1/2 xx b xx h`
	`= 1/2 xx 7 xx 4`
	`= 14\ text(m²)`

Measurement, NAP-G3-NC29 SA

The length of this rectangle is one and a half times its height.

The perimeter of the rectangle is 40 centimetres.

What is the area of the rectangle?

square centimetres

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`96\ text(cm²)`

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`text(Let)\ \ \ x`	`=\ text(height)`
`3/2 x`	`=\ text(length)`

`2 xx (x + 3/2 x)`	`= 40`
`5x`	`= 40`
`x`	`= 8`

`:.\ text(Area)`	`= x(3/2 x)`
	`= 8 xx 12`
	`= 96\ text(cm²)`

Measurement, NAP-G3-CA30 SA

Sam moves into a new rectangular office that measures 4.5 m × 3 m.

He decides to cover the floor with square carpet tiles.

How many boxes of carpet tiles does Sam need to order?

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`24\ text(boxes)`

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`text(Area of office in the number of tiles)`

`= 4.5/0.25 xx 3/0.25`

`= 18\ text(tiles) xx 12\ text(tiles)`

`= 216\ text(tiles)`

`:.\ text(Number of boxes to order)`

`= 216/9`

`= 24\ text(boxes)`