Area & Perimeter

Here is a trapezium drawn on a centimetre grid.

On the grid, draw a triangle equal in area to this trapezium.

The diagram shows a trapezium  and two identical semicircles.

The centre of each semicircle is on .

Work out the area of the shaded region.
Give your answer correct to 3 significant figures.

The diagram shows a wall in the shape of a trapezium.

Karen is going to cover this part of the wall with tiles.
Each tile is rectangular, 15 cm by 7.5 cm.

Tiles are sold in packs.
There are 9 tiles in each pack.

Karen divides the area of this wall by the area of a tile to work out an estimate for the number of tiles she needs to buy.

Use Karen's method to work out the estimate for the number of packs of tiles she needs to buy.

Karen is advised to buy 10% more tiles than she estimated.
Buying 10% more tiles will affect the number of the tiles Karen needs to buy.

She assumes she will need to buy 10% more packs of tiles.

Is Karen's assumption correct?
You must show your working.

Here is a diagram showing a rectangle, , and a circle.

 is a diameter of the circle.

Calculate the percentage of the area of the rectangle that is shaded.
Give your answer correct to 1 decimal place.

The diagram shows a path around a pond.

The pond is in the shape of a rectangle with length 7m and width 4m.
The path is 3m wide.

Ali is going to cover the path with gravel.
One bag of gravel will cover 10 m² of the path.

How many bags of gravel does Ali need to buy?
You must show your working.

Mr Weaver's garden is in the shape of a rectangle.

In the garden

	there is a patio in the shape of a rectangle
and	two ponds in the shape of circles with diameter 3.8 m.

The rest of the garden is grass.

Mr Weaver is going to spread fertiliser over all the grass.
One box of fertiliser will cover 25 m² of grass.

How many boxes of fertiliser does Mr Weaver need?
You must show your working.

The diagram shows the plan of a playground.

Bill is going to cover the playground with tarmac.
It costs £2.56 to cover each square metre with tarmac.

Work out the total cost of the tarmac Bill needs.

The diagram shows the plan of a floor.

Angie is going to varnish the floor.

She needs 1 litre of varnish for 5m² of floor.
There are 2.5 litres of varnish in each tin of varnish.

Angie has 3 tins of varnish.

Does she have enough varnish for all the floor?
You must show all your working.

This rectangular frame is made from 5 straight pieces of metal.

The weight of the metal is 1.5 kg per metre.

Work out the total weight of the metal in the frame.

 is a right angled triangle.

All measurements are given in centimetres.
is the point on  such that 

Work out the exact area, in cm², of the shaded region.

Here are two rectangles.

The perimeter of  is 26 cm.
The area of  is 45 cm².

Find the length of .

...................................... cm

The shaded shape is made using three identical right-angled triangles and a square.

Work out the perimeter of the shaded shape.

...................................................... cm

Here is a hexagon .

is parallel to .
Work out the area of hexagon .

....................................... 

The shorter side of a parallelogram has length 6.5 cm

The length of the shorter side is  of the perimeter.

Work out the length of the longer side.

The diagram shows a wall.

The area of the wall is 39.2 m²

Work out the length of the wall.

..........................m

The line  is a tangent to the circle  at the point .
is the point (2, 6).

The line  crosses the -axis at the point .

Work out the area of triangle .

The diagram shows a shaded region formed by removing an equilateral trianglefrom a regular hexagon .

The points and lie on such that .

Given that the area of region is work out the length of .

......................................................

The diagram shows one face of a wall.
This face is in the shape of a pentagon with exactly one line of symmetry.

Omondi is going to paint this face of the wall once.
He has to buy all the paint that he needs to use.

The paint in each tin of paint Omondi is going to buy will cover 16 m² of the face of the wall.

Work out the least number of tins of paint Omondi will need to buy.
Show your working clearly.

The diagram shows an isosceles triangle.

The area of the triangle is 

Work out the perimeter of the triangle.
Give your answer correct to  significant figures.

   cm 

Calvin has  identical rectangular tiles.
He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the diagram below.

Work out the area of the shaded rectangle.

and are points on a circle with centre .

is a diameter of the circle.



Angle

Work out the total area of the regions shown shaded in the diagram.
Give your answer correct to 3 significant figures.

The diagram shows a regular octagon 

Each side of the octagon has length 

Find the area of the shaded region 
Give your answer correct to the nearest 

.............................................  

The diagram shows a circle and a trapezium.

The height of the trapezium is .

The area of the circle is equal to the area of the trapezium.

Work out the value of .
Give your answer correct to 1 decimal place.

The diagram shows a shaded shape made from a semicircle and a right-angled triangle .

is the diameter of the semicircle .

Work out the perimeter of the shaded shape.
Give your answer correct to 3 significant figures.

....................

The diagram shows two circles such that the region , shown shaded in the diagram, is the region common to both circles.

One of the circles has centre and radius 5cm.
The other circle has centre and radius 4 cm.
Angle

Calculate the area of region .
Give your answer correct to 3 significant figures.

...................................................... cm² 

Here is an L-shape.

All dimensions are in centimetres.

The area of the L-shape is 65 cm²

Work out the value of.

The diagram shows a logo.

and are congruent triangles.
is a sector of a circle, centre .

Show that the area of the logo is 510 cm² to 2 significant figures.

The diagram shows Jane’s lawn.
It is in the shape of a square of side 36m and three semi-circles.

She is going to spread fertiliser on the lawn at a rate of 30g per square metre.
The fertiliser is only sold in 10kg bags costing £15.80 each.

Calculate the cost of buying the bags of fertiliser for her lawn.
You must show all your working.

£ ........................................................

ABCD is a trapezium.

The perimeter of the trapezium is 56 cm.
The ratio AD : AB : DC : BC = 5 : 12 : 6 : 5.

Calculate the area of the trapezium.
Show your working.

..................................cm² 

In the diagram, the square and the trapezium share a common side of length x cm.

The area of the square is equal to the area of the trapezium.

Work out the value of x.

x = .................. 

Here is the floor plan of a rectangular room.

Tim buys carpet tiles for this room.

Each tile is a square measuring 50cm by 50cm.
The tiles are only sold in packs of ten.
Each pack costs £20.
Tim pays for fitting at a rate of £7.50 per square metre, with any fraction of a square metre rounded up.

Work out the total cost of the tiles and fitting.

£ .......................... 

The lengths of the sides of two squares are integers, when measured in cm.
The difference between the areas of the two squares is 36cm².

Find the lengths of the sides of the two squares.

.............................. cm
.............................. cm