Area Questions
1. Calculate the area of the shaded region below, given that AC is an arc of a circle centre B. AB=BC=14cm CD=8cm and angle ABD = 750 (4 mks)
2 The scale of a map is 1:50000. A lake on the map is 6.16cm2. find the actual area of the lake in hactares. (3mks)
3. The figure below is a rhombus ABCD of sides 4cm. BD is an arc of circle centre C. Given that ABC = 1380. Find the area of shaded region. (3mks)
4. The figure below sows the shape of Kamau’s farm with dimensions shown in meters
Find the area of Kamau’s farm in hectares (3mks)
5. In the figure below AB and AC are tangents to the circle centre O at B and C respectively,
the angle AOC = 600
Calculate
(a) The length of AC (2 marks)
6. The figure below shows the floor of a hall. A part of this floor is in the shape of a rectangle of length 20m and width 16m and the rest is a segment of a circle of radius 12m. Use the figure to find:-
(a) The size of angle COD (2mks)
(b) The area of figure DABCO (4mks)
(c) Area of sector ODC (2mks)
(d) Area of the floor of the house. (2mks)
7. The circle below whose area is 18.05cm2 circumscribes a triangle ABC where AB = 6.3cm, BC = 5.7cm and AC = 4.8cm. Find the area of the shaded part (4 mks)
8. In the figure below, PQRS is a rectangle in which PS=10k cm and PQ = 6k cm. M and N are midpoints of QR and RS respectively
- Find the are of the shaded region (4 marks)
- Given that the area of the triangle MNR = 30 cm2. find the dimensions of the rectangle (2 marks)
- Calculate the sizes of angles
and giving your answer to 2 decimal places (4 marks)
and 
giving your answer to 2 decimal places (4 marks)9. The figure below shows two circles each of radius 10.5 cm with centres A and B. the circles touch each other at T
Given that angle XAD =angle YBC = 1600 and lines XY, ATB and DC are parallel, calculate the area of:
- The minor sector AXTD (2 marks)
- Figure AXYBCD (6marks)
- The shaded region (2 marks)
10. A student took the measurements of his classroom and gave the width as 7m and the length as 9m.
If there is an error of 2% in each measurement, determine the greatest value of x + y
x
if x and y are the width and length of the classroom respectively.
Give your answer to 4 decimal places.
11. The floor of a room is in the shape of a rectangle 10.5 m long by 6 m wide. Square tiles of
length 30 cm are to be fitted onto the floor.
(a) Calculate the number of tiles needed for the floor.
(b) A dealer wishes to buy enough tiles for fifteen such rooms. The tiles are packed in cartons
each containing 20 tiles. The cost of each carton is Kshs. 800. Calculate
(i) the total cost of the tiles.
(ii) If in addition, the dealer spends Kshs. 2,000 and Kshs. 600 on transport and subsistence
respectively, at what price should he sell each carton in order to make a profit of 12.5%
(Give your answer to the nearest Kshs.)
12. The figure below is a circle of radius 5cm. Points A, B and C are the vertices of the triangle
ABC in which ABC = 60o and ACB=50o which is in the circle. Calculate the area of ABC )
13. Mr.Wanyama has a plot that is in a triangular form. The plot measures 170m, 190m
and 210m, but the altitudes of the plot as well as the angles are not known. Find the area
of the plot in hectares
14. Three sirens wail at intervals of thirty minutes, fifty minutes and thirty five minutes.
If they wail together at 7.18a.m on Monday, what time and day will they next wail together?
15. A farmer decides to put two-thirds of his farm under crops. Of this, he put a quarter under
maize and four-fifths of the remainder under beans. The rest is planted with carrots.
If 0.9acres are under carrots, find the total area of the farm
16. Find the area of the circle sector.
Area Answers
1 |
| M1 M1 M1 A1 | |
2. | LSF 1 cm rep 50000cm 1cm rep 500m ASF 1cm2 rep 250000m2 Area = = 154ha | B1 M1 A1 | ASF given |
03 | |||
3. | Area = 4 x 4sin 420 – = 10.71 – 5.867 = 4.796 | M1 M1 A1 | area of rhombus & sector difference in area |
03 |
5. (a) Tan 600 = AC
5cm M1
AC = 8.6605CM A1
(b) A = ½ x 5 x 8.6605 M1
A = 21.65125 A1
- 60/360 x r2
60/360 x 3.142 x 25 M1
= 13.091cm2 A1
(d) Area of shaded part
Δ COA = Δ OBA, sector OCD = OCB
21.65 x 2 = 43.3025cm2 M1
13.091 x 2 = 26.182cm2 M1
Area of shaded part
43.3025 – 26.182 M1
= 17.11225cm2 A1
10
6. |
½ x 200 x 120 = 12,000 160 x ½ x 50 = 4000 ½ x 50 x 40 = 1000 ½ x 50 x 100 = 2500 ½ x 180 x 70 = 6300 ½ x 140 x 80 = 5600 ½ x 100 x 60 = 3000 34400m2 = 3.44ha | B1 B1 B1 B1 B1 M1 M1 M1 A1 B1 | For AH for offset div for AH Offsets to AH Complete diagram | ||
10 | |||||
7. |
| B1 M1 A1 B1 | |||
04 | |||||
8 |
Area of the rectangle= 60k2 Area of unshaded part parts Area of shaded part = 60k2 – 37.5k2 = 22.5k2 b) Dimensions = 20m by 12 cm
| M1 M1 M1 A1 M1 A1 M1 A1 M1 A1 | |||
10 | |||||
9 |
D C 10.5 h 10.5 800 A T x B Area of AXYBCD
= 396.58-154 = 88.58 cm2 | M1 A1 B1 B1 M1 A1 M1 A1 M1 A1 | |||
10 | |||||
10. M x m value = 2.655 + 6.415
6.405 – 2.655
= 9.07
3.75
= 2.4187
11. (a) Number of tiles = 10.5 x 6
to cover the room 0.3 x 0.3
= 700 tiles
(b) (i) 15 x 700 tiles
15 x 700 cartons
20
Cost = 15 x 700 x 800
20
Cost = Kshs. 420,000
(ii) Other expenses = 2000 + 600 = 2600/=
Total expenses = Kshs. 420,000 + 2600
= Kshs. 422600
Selling price = 112.5 x 422600
100
= Kshs. 475, 425
Selling price per tile = 475,425
525 x 20
= 45.27
= Kshs. 45.00
12. AC = 10 = AC = 8.66
Sin 60o
A70o, BC = 10 = BC = 8.91
Sin 70o
Area = ½ x 8.66 x 8.91 sin 50o
= 27.28
13. S = ½ (170 + 190 + 210)
S = 285
Area = 285 (285 – 170) (285 – 190) (285 – 210)
= 2865 x 115 x 95 x75
= 15281m2
10,000
= 1.528ha
14. LCM of 30, 50 and 35 mins
30 = 2 x 3 x 5
35 = 5x 7
50 = 2 x 52
Into hrs (1050) hrs = 17.5hrs
60
Next wail together at 7:18
+ 17:30
24:48
= at 1. 48 a.m on Tuesday
15. Maize – ¼ x 2 = 1
3 6
Remainder – 2 – 1 = 3 = ½
3 6 6
Beans – 4 x ½ = 2
5 5
carrrots – 1 x 1 = 1
5 2 10
Let total area of farm be x acres
1 x = 0.9
10
x = 0.9 x 10 = 9acres
