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Ten points are marked along the edge of a circle, and each point is connected to the center, which is 35 cm away. What is the combined fencing length from the center to any two such points, and what area is enclosed between them?
a) 180
b) 200
c) 220
d) 240
e) None of these
Option c – 220
Equilateral triangles are drawn outward along each side of a hexagon. The combined area of all these triangles is in what ratio to the area of the hexagon?
a) ½
b) ¼
c) 2
d) 1
e) Data inadequate
Option d – 1
A trapezium has a total boundary length of 130 cm. One of the parallel sides is 40 cm, and each of the non-parallel sides is 17 cm. What is its area?
a) 415
b) 623
c) 795
d) 815
e) None of these
Option c – 795
A circle is precisely cut out from a rectangular sheet that is 20 cm long, leaving 154 cm² removed. What is the remaining area on the sheet?
a) 36
b) 35
c) 40
d) 45
e) None of these
Option d – 45
A wire 49 cm long is used to outline a hexagon, with an equilateral triangle attached on one of its sides. What is the area of the entire figure?
a) 250
b) 130
c) 150
d) 240
e) 270
Option c – 150
The diagonals of a rhombus measure 16 cm and 30 cm. What is its total boundary length?
a) 30
b) 16
c) 14
d) 68
Option d – 68
A rectangle of dimensions 60 cm by 28 cm has the largest circle inscribed within it. What is the uncovered area of the rectangle?
a) 400
b) 825
c) 1060
d) 1300
e) None of these
Option c – 1060
A square field measuring 9 hectares is surrounded by three layers of fencing. How much wire is needed in kilometers?
a) 3.6
b) 36
c) 360
d) 3600
e) None of these
Option b – 36
Ten points are marked on a circle, each joined to the center at a distance of 35 cm. What is the fencing length between the center and any two points?
a) 92
b) 70
c) 82
d) 68
e) None of these
Option a – 92
What is the circumference of a circle that has an area of 1386 square meters?
a) 132
b) 66
c) 108
d) 88
e) None of these
Option a – 132
A rhombus has diagonals measuring 48 m and 14 m. What is its perimeter?
a) 90
b) 100
c) 120
d) 80
e) None of these
Option b – 100
A parallelogram has side lengths of 30 m and 20 m, with an included angle of 30°. What is its area in square meters?
a) 200
b) 250
c) 275
d) 300
e) None of these
Option d – 300
A parallelogram with sides 28 m and 15 m has a perpendicular height of 12 m. What is its area?
a) 236
b) 300
c) 336
d) 363
e) None of these
Option c – 336
A circle with a diameter of 14 cm is tightly enclosed in a square. How much area remains uncovered in the square?
a) 42
b) 28
c) 32
d) 36
e) None of these
Option a – 42
A triangle has side lengths of 50 cm, 60 cm, and 70 cm. What is its area in square centimeters?
a) 1100
b) 1300
c) 1500
d) 1700
e) None of these
Option c – 1500
A square and a rectangle each have a perimeter of 100 cm. What is the difference between their areas?
a) 100
b) Data inadequate
c) Can’t say
d) No difference
e) None of these
Option b – Data inadequate
What is the length of the diagonal of a rectangular field that measures 240 m by 70 m?
a) 240
b) 250
c) 260
d) 270
e) None of these
Option b – 250
A square plot of land has an area of 4 hectares. What is the length of its diagonal?
a) 300
b) 250
c) 325
d) 280
e) None of these
Option d – 280
A rectangular ground measuring 200 m by 60 m has two intersecting roads each 5 m wide. What is the area occupied by the roads?
a) 1300
b) 25
c) 1325
d) 1275
e) None of these
Option d – 1275
A 300 m × 50 m field has two metalled cross roads 5 m wide running through it. What is the remaining unpaved area in square meters?
a) 12225
b) 12750
c) 13225
d) 13500
e) None of these
Option c – 13225
A circle has an area of 2464 m². What is its diameter?
a) 7
b) 14
c) 28
d) 56
e) None of these
Option d – 56
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