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Class 7 Mathematics area of varied shapes questions and answers
What is the area of a square garden whose perimeter is 116 metres?
A. 29
m
2
B. 58
m
2
C. 841
m
2
D. 3364
m
2
(2m 12s)
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1.
The perimeter of a rectangular field is 14 m. If one of the sides is 3, what is the area of the field? A. 21
m
2
B. 33
m
2
C. 42
m
2
D. 12
m
2
2.
A circular cut-out of diameter 14 cm is removed from a square board of length 30 cm. What is the area of the piece of board that remains? (Take
π
=
22
7
) A. 856
c
m
2
B. 154
c
m
2
C. 746
c
m
2
D. 284
c
m
2
3.
The figure below shows a square WXYZ drawn inside a circle centre O. The radius of the circle is 3.5cm. What is the area of the shaded part? (Take
π
=
22
7
) A. 38.5
c
m
2
B. 26.25
c
m
2
C. 24.5
c
m
2
D. 14.0
c
m
2
4.
What is the area of the shaded region in the diagram below? (Take
π
=
22
7
) A. 269.5
c
m
2
B. 211.75
c
m
2
C. 173.25
c
m
2
D. 134.75
c
m
2
5.
The figure below represents a square enclosed in a circle of radius 7cm. What is the area of the shaded parts? (Take
π
=
22
7
) A. 28
c
m
2
B. 56
c
m
2
C. 98
c
m
2
D. 154
c
m
2
6.
In the figure below,XY,YZ and XZ are diameters of circles. What is the area of shaded part? (Take
π
=
22
7
) A. 462
c
m
2
B. 385
c
m
2
C. 308
c
m
2
D. 231
c
m
2
7.
In the diagram below,AB is the diameter of a semi-circle. AB =10cm, AC=8cm, BC=6cm and angle ACB=
90
0
What is the area of the shaded part? (Take
π
=3.14) A. 54.50
c
m
2
B. 39.25
c
m
2
C. 24.00
c
m
2
D. 15.25
c
m
2
8.
The diagram below represents Mwau’s shamba. What is the size of Mwau’s shamba in hectares? A. 1.175ha B. 1.325ha C. 2.0ha D. 11.75ha
9.
In the figure below, angle BAF is a right angle. Line CB is parallel to EF and CB=EF=7cm. line BA=4cm and AF=3cm.EDC is a semicircle of diameter 5cm. What is the area of the figure in square centimetres? (Take
π
=
22
7
) A. 50.8125 B. 56.8125 C. 60.6250 D. 80.2500
10.
A rectangular plot measures 64 m by 16m. What would be the length of the side of a square plot with the same area? A. 32m B. 40m C. 512m D. 1024m
11.
A plot of land is made up of a semi-circle and a rectangle. The semi-circle has a diameter of 14m while the rectangle measures 20m by 5. What is the area of the plot? (Take
π
=
22
7
) A. 122
m
2
B. 177
m
2
C. 254
m
2
D. 408
m
2
12.
The two parallel sides of a trapezium measures 16 cm and 12 c. the perpendicular distance between the parallel sides is 8cm. what is the area of the trapezium? A. 112
c
m
2
B. 768
c
m
2
C. 224
c
m
2
D. 160
c
m
2
13.
The figure below represents a quarter of a circle centre O. The radius of the circle is 7cm. What is the area of the shaded part? (Take
π
=
22
7
) A. 24.5
c
m
2
B. 14
c
m
2
C. 28.5
c
m
2
D. 63
c
m
2
14.
The figure below is a trapezium. Lines HG=11cm,GF=5cm,EF=15cm and HE=3cm. line EF is parallel to HG and angle FEH=angle EHG=
90
0
. What is the area of the figure? A. 78
c
m
2
B. 39
c
m
2
C. 65
c
m
2
D. 75
c
m
2
15.
The figure below represents a table mat made up of a rectangle and four semicircle. The rectangle measures 14cm by 7 cm What is the area of the table mat? (Take
π
=
22
7
) A. 192
1
2
c
m
2
B.868
c
m
2
C.
290
1
2
c
m
2
D.
194
1
2
c
m
2
16.
The figure shown below, is formed by two right- angled triangles ABD and BCD. What is the area of the triangle BCD? A. 300
c
m
2
B. 180
c
m
2
C. 84
c
m
2
D. 150
c
m
2
17.
A flower garden is made up a semi-circle of diameter 14m, a rectangle measuring 20 metres long and 14metres wide and a quarter of circle of radius 14m. What is the area of the flower garden in
m
2
.(
t
a
k
e
π
=
22
7
)? A. 742 B. 665 C. 511 D.
395
1
2
18.
A lawn is in the form of a rectangle and two semicircles. The rectangle is 22 m long and 6 m wide. The widths of the rectangle are also the diameters of the semi-circles. What is the area of the lawn in
m
2
?(Take
π
=
22
7
) A. 245
1
7
B. 188
4
7
C. 160
2
7
D. 28
2
7
19.
The diagram below represents a flower garden. What is the area of the flower garden in
m
2
? A. 36 B. 60 C. 65 D. 120
20.
The shaded figure below was obtained from a rectangular piece of paper from which a semi-circle of diameter 14cm was removed and another semi-circle of diameter 7cm added. What is the area of the shaded figure? (Take
π
=
22
7
) A.
229
1
4
c
m
2
B.
306
1
4
c
m
2
C.
152
1
4
c
m
2
D.
113
3
4
c
m
2
21.
What is the area of a square garden whose perimeter is 116 metres? A. 29
m
2
B. 58
m
2
C. 841
m
2
D. 3364
m
2
22.
The figure below represents a vegetable garden consisting of a square and four semi-circles each of diameter 4.2m. What is the area of the garden in square metres? (Take
π
=
22
7
) A. 69.6 B. 225 C. 252.72 D. 335.88
23.
In triangle PQR below, PQ=8cm, PM=MQ and PR=RQ=5cm. What is the area of the triangle? A.
7
1
2
c
m
2
B.
6
c
m
2
C.
12
1
2
c
m
2
D.
12
c
m
2
24.
A rectangle 25cm long and 12 cm wide has the same area as a triangle whose is 10cm. What is the length of the base of the triangle. A. 15cm B. 30cm C. 60cm D. 300cm
25.
The height of an isosceles triangle is 4cm. Each of the two equal sides measures 5cm. What is the area of the triangle? A. 6
c
m
2
B. 12
c
m
2
C. 15
c
m
2
D. 24
c
m
2
26.
The diagram below is a trapezium MNPQ. Line MQ is parallel to line NP. The length of line MQ=8cm and that of line NR=7cm. The perpendicular line MR =12cm. If the area of the trapezium is
198
c
m
2
, what is the length of RP? A. 15cm B. 18cm C. 25cm D. 32cm
27.
The perimeter of the isosceles triangle QRS shown below is 48cm. The base of the triangle is 18cm. What is the area of the triangle? A. 54
c
m
2
B. 108
c
m
2
C. 135
c
m
2
D. 435
c
m
2
28.
The diagram below represents a vegetable garden which is in the shape of a rectangle and semicircles. What is the area of the garden in square metres? (Take
π
=
22
7
) A. 693 B. 1008 C. 1085 D. 1162
29.
What is the area of the figure shown below? A. 24
c
m
2
B. 36
c
m
2
C. 34
c
m
2
D. 40
c
m
2
30.
The figure below represents a flower garden in the shape a quarter of a circle of radius 7m and a right angled triangle. What is the area of the flower garden? (Take
π
=
22
7
) A. 95
m
2
B. 108
1
2
m
2
C. 122
1
2
m
2
D. 147
m
2
31.
The perimeter of a triangle is 32cm. Two sides of the triangle measure 10cm and 12cm. What is the area of the triangle? A. 24 B. 40 C. 48 D. 50
32.
The area of a square garden is
3136
m
2
. What is the length of one side of the garden in metres? A. 14 B. 56 C. 784 D. 1568
33.
The perimeter of a rectangular field is 56m. The length of one of its sides is 7m. What is the area of the field? A. 392
m
2
B. 294
m
2
C. 171
m
2
D. 147
m
2
34.
A design was made up of straight edges of length 2.6cm and arcs of circles of radii 1.4cm as shown in the figure below. What is the area of the design? (Take
π
=
22
7
) A. 16.00
c
m
2
B. 22.16
c
m
2
C. 25.24
c
m
2
D. 28.32
c
m
2
35.
A plot of land is in the shape of a rhombus of side 200m. The length of one of the diagonals is 240m. what is the area of the plot in hectares? A. 3.84 B. 4 C. 4.8 D. 7.68
36.
The figure KLMN drawn below is a square of sides 40cm. What is the area of the shaded part? (Take
π
=3.14) A. 1256
c
m
2
B. 972
c
m
2
C. 628
c
m
2
D. 344
c
m
2
37.
A piece of land, 7.25ha is to be divided into 0.125ha plots. If two houses were to be built in each plot, how many houses would be built? A. 11.6 B. 29 C. 58 D. 116
38.
The diagram below represents a piece of land in the shape of a trapezium and semi-circle. What is the area of piece of land in ares? (Take
π
=
22
7
) A. 4242 B. 70.14 C. 42.42 D. 32.34
39.
A conference room measures 24m by 12m. Square carpets of 4 metres long, each costing sh.12000 were used to completely cover the floor. How much did it cost to cover the floor? A. Sh. 48000 B. Sh. 72000 C. Sh. 216000 D. Sh. 864000
40.
The diagram below shows Kamau’s plot of land. The dimensions are shown in the diagram What is the area of the plot? A. 60
m
2
B. 34
m
2
C. 72
m
2
D. 48
m
2
41.
What is the area of the shaded part in the figure below? A. 1200
m
2
B. 1500
m
2
C. 2400
m
2
D. 900
m
2
42.
What is the area of the figure given below? A. 13400
c
m
2
B. 16400
c
m
2
C. 12200
c
m
2
D. 23600
c
m
2
43.
The figure below represents a plot bound by two straight edges and a semicircle. What is the area of the plot? (Take =3.142) A. 102.550
m
2
B. 63.275
m
2
C. 39.710
m
2
D. 39.275
m
2
44.
The figure below represents a circle inscribed in a circle of side 14 cm. What is the area of the shaded part in
c
m
2
(Take
22
7
) A. 10.5 B. 38.5 C. 42.0 D. 49.0
45.
The shaded parts in the figure below represents Kamau’s plot of land. What is the area of the plot in hectares? A. 0.0675 B. 0.3150 C. 0.4500 D. 0.3825
46.
In a trapezium, the two parallel sides are 6 cm and 8 cm long. The perpendicular distance between the parallel sides is 4 cm. What is the area of the trapezium? A.24
c
m
2
28
c
m
2
32
c
m
2
56
c
m
2
47.
The figure below represents a farm. What is the area of the farm in square metres? A. 2209 B. 2244 C. 2293 D. 2377
48.
The figure below represents a piece of land. What is the area of the piece of land? A. 6300
m
2
B. 4350
m
2
C. 3600
m
2
D. 6550
m
2
49.
The figure below represents a flower garden in the shape of a triangle and a semicircle. What is the area of the garden? (Take
π
=
22
7
) A.
102
4
7
m
2
B.
29
5
7
m
2
C.
63
2
7
m
2
D.
39
2
7
m
2
50.
Triangle RST below is an isosceles triangle. The length RT=RS=10cm and ST=12cm. What is the area of the triangle? A. 32
c
m
2
B. 48
c
m
2
C. 24
c
m
2
D. 60
c
m
2
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