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Area Problems

Area Problems
The length of each side of an equilateral triangle having an area of 4?3 cm 2 is?

3 cm
4/?3 cm
4 cm
?3/4 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Area of equilateral triangle = ?3/4 a2 = 4?3.? a2 = 16? a = 4 cm

Area Problems
A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6: 5 . The smaller side of the rectangle is?

132 cm
30 cm
72 cm
60 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Perimeter of rectangle = Circumference of circle = 2?r=2 x ( 22/7 ) x 42= 264 cm Now perimeter of rectangle = 2 x ( 6a + 5a )? 2 x (6a + 5a) = 264? a = 12Smaller side of rectangle = 5a = 60 cm

Area Problems
The area of a trapezium is 384 sq.cm. If its parallel sides in ratio 3 : 5 and the perpendicular distance between them be 12 cm. The smaller of parallel sides is?

24 cm
32 cm
40 cm
16 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let the parallel sides be 3a and 5a.So Area of trapezium = 1/2 x sum of parallel side x perpendicular distance between them.? 1/2 (3a +5a) x 12 = 384? 8a = 64? a =8? Smaller side = 3x = 3 x 8 = 24 cm.

Area Problems
The radius of a circle is so increased that its circumference increased by 5%. The area of the circle, then increases by

11.25%
10.5 %
10.25%
12.5%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Increase in circumference of circle = 5%? Increase in radius is also 5%.Now, increase in area of circle = 2a + (a2/100) %Where, a = increase in radius= 2 x 5 + (5 x 5)/100 % = 10.25%

Area Problems
Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 154 sq m.

13 m
8 m
7 m
12 m

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Length of to the rope = Radius of circle According to the question,?r2 = 154 ? r2 = 154 x (7/22) = 7 x 7 = 49 ? r = ?49 = 7 m

Area Problems
If the diagonal of a square is double, how does the area of the square change?

Becomes two fold
None of these
Becomes four fold
Becomes three fold

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Ratio of the areas = area of original square / area of new square = [ d2 / 2 ] / [ (2d)2 / 2 ] = 1/4? New area becomes 4 fold.

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