Perimeter And Area - 2D Test

Result

Perimeter And Area - 2D Test - 9

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Question 1
1 / -0

A rectangular sheet of paper, when halved by folding it at the mid-point of its longer side, results in a rectangle which has longer and shorter sides in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2 units, then what is the area of the smaller rectangle?

A
sq. units

B
sq. units

C
sq. units

D
3sq. units

Solution

Option (2) is correct.
Question 2
1 / -0

In the figure given below, what is the area of the shaded region (in cm²), if the radius of the circle is 4 cm?

A
12

B
32

C
36 – 8

D
8

Solution

Option (4) is correct.
Question 3
1 / -0

The ratio of the areas of a square and the square drawn on its diagonal is

A
1 : 4

B
2 : 1

C
1 : 2

D
1 : 3

Solution

Option (3) is correct.
Question 4
1 / -0

A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. It is given that AC = 2 cm and CD = 6 cm. What will be the area of the semi-circle (in sq. cm)?

A
32

B
50

C
40.5

D
81

Solution

Option (2) is correct.
Question 5
1 / -0

A side of a square is 2 m. Its corners are cut in such a way so as to form an octagon with all sides equal. What is the length of each side of the octagon in metres?

A

B

C

D

Solution

Option (2) is correct.
Question 6
1 / -0

In the above diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the area of the triangle CEF to that of the rectangle?

A

B

C

D

Solution

Option (1) is correct.
Question 7
1 / -0

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

A
: 2

B
1 :

C
2 : 5

D
3 : 4

Solution

Option (4) is correct.
Question 8
1 / -0

The perimeter of a square, whose area is equal to that of a circle with perimeter 2x, is

A
2x units

B
units

C
4 units

D
4x units

Solution

Option (4) is correct.
Question 9
1 / -0

A wire, bent in the form of a square, encloses an area of 121 cm². If the same wire is bent to form a circle, then what will be the enclosed area?

A
154 cm²

B
159 cm²

C
161 cm²

D
168 cm²

Solution

Option (1) is correct.
Question 10
1 / -0

Two identical circles intersect so that their centres and the points, at which they intersect, form a square of side measuring 1 cm. What is the area (in sq. cm) of the portion that is common to the two circles?

A

B

C

D

Solution

Option (2) is correct.
Question 11
1 / -0

Two sides of a plot measure 32 m and 24 m, and the angle between them is a right angle. The other two sides measure 25 m each and the other three angles are not right angles. What is the area of the plot (in m²)?

A
768

B
534

C
696.5

D
684

Solution

Option (4) is correct.
Question 12
1 / -0

Given, ABC = 90° = DCH = DOE = EHK = FKL = GLM = LMN, and AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN.

What is the magnitude of FGO in the figure given above?

A
30°

B
45°

C
60°

D
None of these

Solution

Option (4) is correct.
Question 13
1 / -0

The area of the quadrilateral PRST is 48 cm². Q is the mid-point of PR and PR || TS. The area of PQT is

A
20 cm²

B
16 cm²

C
8 cm²

D
12 cm²

Solution

Option (2) is correct.
Question 14
1 / -0

Four horses are tethered at the four corners of a square plot for grazing such that, each one of them can just reach the horses at the adjacent corners. The area of the plot left ungrazed is

A
675.5 m²

B
780.6 m²

C
785.8 m²

D
None of these

Solution

Option (4) is correct.
Question 15
1 / -0

The figure given below shows an octagon. What is the area of the octagon?

A
14 sq. units

B
7 sq. units

C
28 sq. units

D
14 sq. units

Solution

Option (3) is correct.
Question 16
1 / -0

Given, ABC = 90° = DCH = DOE = EHK = FKL = GLM = LMN, and AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN.

What is the ratio of the areas of the two quadrilaterals ABCD and DEFG?

A
1 : 2

B
2 : 1

C
12 : 7

D
7 : 12

Solution

Option (3) is correct.
Question 17
1 / -0

Two parallelograms are on the same base and between the same parallels. The ratio of their areas is

A
2 : 1

B
1 : 2

C
1 : 1

D
3 : 1

Solution

Option (3) is correct.
Question 18
1 / -0

If the number of square inches in the area of a square is equal to the number of inches in its circumference, then what is the length of the diagonal of the square?

A
4 inches

B
4inches

C
3inches

D
inches

Solution

Option (2) is correct.