Area And Perimeter

42.
A paper ring is made by cutting round a circle of radius 3.5 cm as shown in the diagram.
3.5 cm 3.5 cm NOT TO SCALE

Use π=227.
Work out the:
(a) area of the ring
(b) total perimeter of the ring
(a) ......................... (b) .........................
Paper 1
44.
The diagram shows a trapezium.
4 cm 8 cm 10 cm NOT TO SCALE

Calculate the area of the trapezium.
.................................
Paper 1
46.
3 cm 2 cm 2 cm 3 cm 1 cm 1 cm NOT TO SCALE

Calculate:
(a) The perimeter,
(b) The area.
(a) ......................... cm [2] (b) ......................... cm2 [2]
Paper 1
48.
The radius of the smaller circle is 3 cm and that of the larger circle is 5 cm.
NOT TO SCALE

Calculate, in terms of π:
(a) the area of the smaller circle,
(b) the area of the shaded region.
(a) ......................... cm2 [1] (b) ......................... cm2 [2]
Paper 1
49.
The diagram shows a rectangle with a semi-circle inside.
The semi-circle touches the sides of the rectangle as shown.
The length of a rectangle is 28 cm and width 14 cm.
28 cm 14 cm NOT TO SCALE

Use π=227.
Calculate:
(a) The area of the unshaded region,
(b) The total perimeter of the semi-circle.
(a) ......................... cm2 [3] (b) ......................... cm [3]
Paper 1
50.
The diagram shows an isosceles triangle ACD.
A C = 8  cm .
A B C D 8 cm NOT TO SCALE
(a) The area of the triangle is 12   cm 2 .
Find the length CD.
(b) Write the value of tan ⁡ D C ^ B .
(a) ......................... cm [3] (b) ......................... [1]
Paper 1
18.
The diagram shows a sector of radius 8 cm. Angle AOB is 90°.
A O B 8 cm NOT TO SCALE

Calculate:
(i) The perimeter of the sector,
......................... cm [2]
(ii) The shaded area.
......................... cm2 [2]
Paper 3
19.
The diagram shows the cross section of a machine. QR = UV.
P Q R S T U V W x 25 cm 15 cm 35 cm 45 cm 115 cm NOT TO SCALE

(b)(i) Calculate the area of the cross section.
......................... cm2 [3]
(ii) The machine is in the form of a prism, k cm long. The prism is completely filled with some material. 1 cubic metre of this material has mass 2 kg. Find an expression, in terms of k, for the mass of the material used.
......................... [2]
Paper 3
20.
The diagram shows a sector AOB. Angle AOB is a right angle and O is the centre.
A O B NOT TO SCALE

(a) The circumference of the circle from which the sector was cut is 13.2 cm. Show that the diameter of the circle from which the sector was cut is 4.2 cm correct to 1 decimal place.
......................... [2]
(b) Calculate:
(i) the length of chord AB,
......................... cm [2]
(ii) the perimeter of the sector AOB,
......................... cm [2]
(iii) the area of the shaded part.
......................... cm2 [3]
Paper 3