Quadrilaterals Test

Result

Quadrilaterals Test - 9

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Question 1
1 / -0

In a rectangle ABCD if diagonal AC = 12 cm, then the diagonal BD is

A
12 cm

B
20 cm

C
5 cm

D
none of these

Solution

In a rectangle, diagonals are equal to each other
AC = BD = 12 cm
AC = BD = 12 cm
Diagonal BD = 12 cm
Question 2
1 / -0

In parallelogram ABCD, DAB = 30⁰, BC = 20 cm and AB = 20 cm. The area of parallelogram is

A
150 cm²

B
200 cm²

C
400 cm²

D
260 cm²

Solution

According to the data given, the diagram is

Find - Area of parallelogram = ?
Sol. In AFD
Sin 30^o =
20 = DF = DF = 10 cm
Area of parallelogram = base height
= 20 DF = 20 10
= 200
Area of parallelogram ABCD is 200 cm²
Question 3
1 / -0

In the given figure, ABCD is a parallelogram. The respective measures of angles x and y are

A
50° and 30°

B
30° and 60°

C
45° and 45°

D
90° and 90°

Solution

CAB = ACD = 50^o [Alternate interior opposite angles]
Since in parallelogram, opposite angels are congruent;
x + y = 50^o + 30^o
50^o+ y = 80^o
y = 30^o
Hence, x = 50^o and y = 30^o
Question 4
1 / -0

A quadrilateral in which diagonals are equal and bisect each other perpendicularly is

A
a square

B
a rhombus, which is not a square

C
a rectangle, which is not a square

D
None of these

Solution

A quadrilateral in which diagonals are equal and bisect each other perpendicularly is a square.
Question 5
1 / -0

The length of a side of a rhombus is 10 m and one of its diagonals is 12 m. The length of the other diagonal is

A
15 m

B
18 m

C
26 m

D
16 m

Solution

As one side of rhombus is 10 m
All sides would also be 10 m because all sides of a rhombus are equal.
And also one of its diagonals is 12 m.
As the diagonals of rhombus bisect each other at right angle
6 m + 6 m = 12 m
Now, In ABE
(10)² = (6)² + (AE)²
100 - 36 = (AE)²
64 = (AE)²
AE = 8 m
length of the other diagonal = 2 x AE = 2 x 8 = 16 m
Question 6
1 / -0

In the parallelogram PQRS, the respective values of SQP and QSP are

A
35° and 70°

B
60° and 45°

C
70° and 35°

D
45° and 70°

Solution

SPQ + RQP = 180° (Sum of adjacent angles of a parallelogram is 180°.)
RQP = 180° - SPQ = 180° - 75° = 105°
SQP = 105° - 70° = 35°
SPQ + PQS + QSP = 180°
QSP = 180° - (75° + 35°) = 70°
Question 7
1 / -0

A quadrilateral is a rhombus but not a square if

A
its diagonals do not bisect each other

B
its diagonals are not perpendicular

C
opposite angles are not equal

D
the length of diagonals are not equal

Solution

A quadrilateral is a rhombus but not a square if the lengths of the diagonals are not equal.
Question 8
1 / -0

ABCD is a parallelogram and BD is a diagonal. If BAD = 70° and BDC = 65°, then DBC is equal to

A
45°

B
65°

C
110°

D
35°

Solution

BAD = 70°
BDC = 65°
DBA = BDC = 65° (Alternating angles as DC || AB and DB is transversal)
DAB + ABC = 180°
ABC = 180° - 70° = 110°

DBC = 110° - 65° = 45°
Question 9
1 / -0

In the parallelogram ABCD, AB = 12 cm. The altitudes corresponding to the sides AB and AD are 9 cm and 8 cm respectively. Find length of AD.

A
13.5 cm

B
14.5 cm

C
15.5 cm

D
16.5 cm

Solution

Area of parallelogram = Base x altitude = 9cm x 12 cm = AD x 8cm
Thus, AD = 13.5 cm
Hence, answer option 1 is correct
Question 10
1 / -0

A quadrilateral is a rectangle but not a square when

A
its diagonals do not bisect each other

B
its diagonals are not perpendicular

C
all angles are not equal

D
its diagonals are not equal

Solution

A quadrilateral is a rectangle but not a square when its diagonals are not perpendicular.
Question 11
1 / -0

The angles of a quadrilateral, taken in order, measure x, x + 20, x + 30 and x + 50 degrees. This quadrilateral is a

A
parallelogram

B
rhombus

C
trapezium

D
square

Solution

Angles of a quadrilateral add up to 360^o.
x + (x + 20) + (x + 30) + (x + 50) = 360^o
4x + 100 = 360
4x = 260
x = 65^o 1^st angle = x = 65^o
2^nd angle = x + 20 = 65 + 20 = 85^o
3^rd angle = x + 30 = 65 + 30 = 95^o
4^th angle = x + 50 = 65 + 50 = 115^o
Out of the given options, options (1), (2) and (4) cannot be possible because all the angles must be equal in a square.
In a rhombus and a parallelogram, opposite angles must be equal.
It must be a trapezium.
Question 12
1 / -0

ABCD is a quadrilateral. If AC and BD bisect each other, then ABCD is a

A
square

B
rectangle

C
parallelogram

D
rhombus

Solution

ABCD is a quadrilateral. AB = BC = CD = DA and A = B = C = D = 90°
Then ABCD can be called A SQUARE.
Question 13
1 / -0

In a parallelogram ABCD, if A = 60°, then B, C and D are respectively

A
50°, 130°, 130°

B
120°, 60°, 120°

C
120°, 120°, 60°

D
130°, 50°, 50°

Solution

In a parallelogram ABCD, if A = 60°, then C = A = 60
Hence option 2 is correct
Question 14
1 / -0

In the given figure, ABCD is a square and ABX is equilateral. In this case, DCX is equal to

A
45⁰

B
30⁰

C
60⁰

D
75⁰
Question 15
1 / -0

ABCD is a parallelogram. The angle bisectors of A and D meet at O. The measure of AOD is

A
45°

B
90°

C
dependent on the angles A and D

D
Cannot be determined from the given data

Solution

A + B + C + D = 360°
We know, A = C and B = D
This implies, 2(A + D) = 360°
A + D = 180°
In triangle AOD,
(A + D) + AOD = 180°
AOD = 90°
Question 16
1 / -0

In a parallelogram ABCD, AB = 4 cm and BC = 8 cm. Each of its diagonals is less than

A
3 cm

B
4 cm

C
7 cm

D
12 cm

Solution

In a parallelogram ABCD, AB = 4 cm and BC = 8 cm. Each of its diagonals is less than 12 cm because if we apply pythagorus theorem on a rectangular parallelogram, the diagonal will comes out to be 9 cm which is less than 12 cm.
Question 17
1 / -0

There is a plane quadrilateral enclosure ABCD. Diagonal AC = 8.2 cm and perpendiculars from B and D to AC are 3.4 cm and 2.6 cm respectively. If 1 cm represents 5 m, then the area enclosed is

A
615 m²

B
123 m²

C
1230 m²

D
12,300 cm²

Solution

Area of quadrilateral, Area of 2 triangles
= Area of ABC + area of ADC
= x 8.2 x 3.4 + x 2.6 x 8.2
= 24.6 cm²
As 1 cm represents 5 m
1 cm² represents 25 m²
24.6 cm² represents 24.6 x 25 m²
= 615 m²
Question 18
1 / -0

ABCD is a quadrilateral. AB = BC = CD = DA and A = B = C = D = 90°. Then ABCD is

A
a rhombus

B
a square

C
a parallelogram

D
all of the above
Question 19
1 / -0

In a square ABCD, its diagonals bisect at O. Then the triangle AOB is

A
an equilateral triangle

B
an isosceles but not right angled triangle

C
a right angled but not an isosceles triangle

D
an isosceles right angled triangle
Question 20
1 / -0

Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is

A
1 : 1

B
: 1

C
1 : 3

D
1 : 2