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NTSE SAT Mathematics - Quadrilaterals Sample Question Paper

SAT Mathematics - Quadrilaterals

Exam Duration: 45 Mins Total Questions : 30

1 )

The length of the diagonal BD of the parallelogram ABCD is 18 cm. If P and Q are the Centroid of the \(\Delta \)ABC and \(\Delta \)ADC repectively then the length of the line segment PQ is

(a)
4 cm
(b)
6cm
(c)
9 cm
(d)
12 cm

2 )

ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If=72^\(\circ\) then the measure of the is

(a)
162^\(\circ\)
(b)
18^\(\circ\)
(c)
108^\(\circ\)
(d)
72^\(\circ\)

3 )

In a quadrilateral ABCD, with unequal sides, if the diagonals AC and BD intersect at right angles then

(a)
AB²+BC²=CD²+DA²
(b)
AB²+CD²=BC²+DA²
(c)
AB²+AD²=BC²+CD²
(d)
AB²+BC²=2(CD²+DA²)

4 )

Measure of each interior angle of a regular polygon can never be

(a)
105^o
(b)
150^o
(c)
108^o
(d)
110^o

5 )

A parallelogram ABCD has sides AB=24 cm; AD= 16cm. The distance between the sides AB and DC is 10cm. Find the distance between the sides AD and BC.

(a)
16 cm
(b)
18 cm
(c)
15 cm
(d)
26 cm

6 )

A square is of area 200 sq.m. Anew square is formed such a way that the length of its diagonal is \(\sqrt 2\) times of the diagonal of the given square. Then the area of the new square formed is

(a)
200\(\sqrt 2\) sq.m
(b)
400\(\sqrt 2\) sq.m
(c)
400 sq.m
(d)
800 sq.m

7 )

If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is

(a)
equal to \(\frac1 4\)
(b)
equal to \(\frac1 2\)
(c)
equal to 1
(d)
greater than 1

8 )

The area of the shaded region is

(a)
49\(\left( 1-\frac { \pi }{ 4 } \right) \)
(b)
49\(\left( \frac { \pi -1}{ 4 } \right) \)
(c)
49\((1-\pi)\)
(d)
none of these

9 )

In the figure, ABCD and PQRS are rectangles, where Q is the mid-point of AC then

(a)
DP=PC
(b)
\(\frac1 3\)PR=\(\frac3 2\)DB
(c)
DP=PQ
(d)
DP=\(\frac1 2\)AC

10 )

A diagonal of a quadrilateral is a line segment that joins two-----vertices of the quadrilateral

(a)
equal
(b)
unequal
(c)
opposite
(d)
none of these

11 )

The sum of the angles of a quadrilateral is-----right angles

(a)
three
(b)
four
(c)
five
(d)
none of these

12 )

A quadrilateral is convex if for each side, the remaining-----lie on the same side of the line containing the side

(a)
Vertices
(b)
opposite
(c)
points
(d)
none of these

13 )

The measure of each angle of a convex 'quadrilateral is-----180^\(\circ\)

(a)
more than
(b)
less than
(c)
more or less than
(d)
none of these

14 )

In parallelogram, two adjacent angles are

(a)
complementary
(b)
supplementary
(c)
acute
(d)
none of these

15 )

Two adjacent angles of a parallelogram are equal. What is the measure of each?

(a)
180^\(\circ\)
(b)
360^\(\circ\)
(c)
90^\(\circ\)
(d)
none of these

16 )

Two adjacent angles of a parallelogram are as 2:3. Find the measure of all the angles

(a)
72^\(\circ\), 108^\(\circ\), 72^\(\circ\), 108^\(\circ\)
(b)
62^\(\circ\), 108^\(\circ\), 62^\(\circ\), 108^\(\circ\)
(c)
108^\(\circ\), 108^\(\circ\), 62^\(\circ\), 62^\(\circ\)
(d)
none of these

17 )

A regular hexagon is inscribed in a circle with centre O. Then, the angle subtended by each side of the square of the centre O is

(a)
80^\(\circ\)
(b)
90^\(\circ\)
(c)
60^\(\circ\)
(d)
45^\(\circ\)

18 )

The ratio of the area of a square to that of the square drawn on its diagonals is

(a)
1:1
(b)
1:2
(c)
1:3
(d)
1:4

19 )

If ABCD is a parallelogram with two adjacent angles A and B equal to each other, then the parallelogram is a

(a)
square
(b)
rhombus
(c)
rectangle
(d)
both A or C

20 )

The length of the diagonals of a rhombus are 16 cm and 12cm. The side of the rhombus is

(a)
12
(b)
13
(c)
14
(d)
15

21 )

In the given figure, ABCD is a trapezium in which AB||DC. If \(\lfloor A\)=55^\(\circ\) and \(\lfloor B\)=70^\(\circ\), then \(\lfloor C\) and \(\lfloor D\) are respectively

(a)
140^\(\circ\), 125^\(\circ\)
(b)
100^\(\circ\), 135^\(\circ\)
(c)
110^\(\circ\), 125^\(\circ\)
(d)
105^\(\circ\), 130^\(\circ\)

22 )

If each interior angle of a regular octagon is 135°, then the exterior angle of octagon is

(a)
65°
(b)
75°
(c)
45°
(d)
none of these

23 )

The sum of all exterior angles of a convex polygon of n sides is

(a)
4 right angles
(b)
\(\frac2 n\)right angles
(c)
(2n-4) right angles
(d)
\(\frac n 2\)right angles

24 )

ABCD is a rhombus. If \(\lfloor ACB\)=46^\(\circ\) , then \(\lfloor ADB\) is equal to

(a)
34^\(\circ\)
(b)
32^\(\circ\)
(c)
124^\(\circ\)
(d)
44^\(\circ\)

25 )

In a parallelogram ABCD, the bisectors of \(\lfloor A\) and \(\lfloor B\) meet at O. Then is equal to

(a)
85^\(\circ\)
(b)
90^\(\circ\)
(c)
110^\(\circ\)
(d)
none of these

26 )

The area of the greatest circle, which can be inscribed in a square whose perimeter is 120 cm is

(a)
\(\frac { 22 }{ 7 } \times { (15) }^{ 2 }cm^{ 2 }\)
(b)
\(\frac { 22 }{ 7 } \times { (\frac7 2) }^{ 2 }cm^{ 2 }\)
(c)
\(\frac { 22 }{ 7 } \times { (\frac{15} 2) }^{ 2 }cm^{ 2 }\)
(d)
\(\frac { 22 }{ 7 } \times { (\frac9 2) }^{ 2 }cm^{ 2 }\)

27 )

The area of a field in the shape of a trapezium measures 1440 m, The perpendicular distance between its parallel sides is 24 m, If the ratio of the parallel sides is 5:3, the length of the longer parallel side is